Neither 'liberalism' nor 'socialism' has a single, core, essentialist meaning.
Liberalism without economics
But if we take John Locke or John Stuart Mill as liberal political theorists, proponents of philosophical liberalism, then this liberalism has no necessary connexion with market capitalism (Darwinian or other), laissez-faire, or any other type of economic system.
I base the following account on Locke's Second Treatise of Civil Government (1689) and A Letter Concerning Toleration (1689 & expanded in later editions), and John Stuart Mill's On Liberty (1859).
The key to philosophical liberalism is the idea of freedom : freedom from the enforcement of a particular religion, freedom from arbitrary government (hence an emphasis on the rule of law), freedom from 'the tyranny of the majority' exerted against the lifestyles of sexual minorities (LGBQT), freedom of opinion, expression and association, and opportunities for personal growth and development created by the freedom to follow a lifeplan of one's own choosing (individually or as a group) so long as one causes no harm to others. There is no such notion as that individuals should be given unrestricted freedom to pursue their own affairs, without regard to the interests of others, and that 'somehow' social harmony and the maximum well-being of society will result.
None of this has ostensibly any economic implications whatever. It is not inherent in the logic of liberalism that one should have the freedom to accumulate property or to control privately the means of production, distribution and exchange, whatever the likes of Hayek and Friedman may say. It is true that Locke in the Second Treatise of Civil Government does license the acquisition of property but he sets limits : one must not accumulate and let spoil and one must leave enough and as good for others.
Compatibility of liberalism with socialism
Mill in fact favoured a form of market socialism in which all capital and property would be socially owned, and leased out to workers' producer co-operatives. He thought the market was a sound test of efficiency, which one may doubt, and that in co-operatives workers managing their own affairs would have opportunities for personal growth and development which were impossible in a hierarchically organised capitalist firm in which they merely did what they were told.
So we see here a contingent link between liberalism and socialism - market socialism. Later liberals such as L.T. Hobhouse extended the state further into the economy by arguing for state provision of education and a redistribution of wealth without which the freedom to follow a lifeplan of one's own choosing would remain an empty, formal freedom for many, even most, citizens. There was no deference to laissez-faire in any of this.
Mill himself, if we take into account his Principles of Political Economy and Chapters on Socialism was prepared to accept :
[state] intervention in such matters as education; the supervision and even public ownership of certain monopolies including gas, water, and railways, aid to voluntary bodies (such as trade unions); the provision of a minimum of subsistence to those in want ... and [state] responsibility for a number of services of 'general convenience' ranging from paving, lighting, and cleaning the streets to subsidizing scientific research, running the Post Office, and building lighthouses. (W.H. Greenleaf, The British Political Tradition, II : The Ideological Heritage, 1988 : 113.) No laissez-faire run amok here, I think, but this agenda for public agencies stood in no contrast or tension with the liberalism of On Liberty (1859).
Mill distinguished between two kinds of socialism. He rejected **revolutionary socialism, the idea that through a violent seizure of power by some class or group existing economic arrangements should be replaced by state (or collective) ownership, operation and direction of the economy. He did not think that the state was adequate to the efficient management of such a task - hence his preference for market socialism. He also, and this is just as important, believed that however and whenever socialism were introduced, it should emerge from the free expression and clash of opinions of the independent thinkers and discriminators that On Liberty celebrates.
The other kind of socialism he recognises is what one might call the islands of socialism approach of thinkers such as Robert Owen and Charles Fourier, with their communes and model communities approach to social transformation.
He prefers his own 'third way' of market socialism and agenda for public agencies set out above.
Tension between liberalism and socialism - (1)
The main worry that many liberals have about state socialism is practical rather than ideological. Under state socialism the state participates to a considerable extent, and perhaps even to the extent of total control, in the ownership and operation of the means of production and the direction of development of the economy. The liberal fear is that since the state already has a monopoly of legal and military power, its strength becomes overwhelming when it adds to this the economic dimension of power over the economy. The liberal fears a Leviathan state.
Views will differ over how realistic this liberal fear is. Reasonably realistic one might say, given certain 20th-century experiences of state socialism. But this is not a judgement for me to make.
Tension between liberalism and socialism - (2)
Socialists believe in freedom. Nothing could be more obvious. However, if socialism places priority on equality, as it will do in certain social and economic conditions of extreme or unjustifiable inequality, the liberal project may be impaired. Liberal freedoms may be a luxury which a state climbing out of poverty cannot afford, at least in the short term. But there is no inherent incompatibility between freedom and equality; and an interlocking of the two should be well within the capabilities of a socialist state once emergency conditions have been removed. (But I can hear cynics saying, 'if they ever are'.)
Tension between liberalism and socialism - (3)
We noted above that liberals such as Hobhouse 'extended the state further into the economy by arguing for state provision of education and a redistribution of wealth without which the freedom to follow a lifeplan of one's own choosing would remain an empty, formal freedom for many, even most, citizens'. If, unlike Mill and Hobhouse, a liberal will not extend the state in this way, and defends only 'formal', legal freedoms - e.g. of expression, opinion and association - then without state intervention to provide economic resources to the least advantaged, such freedoms will appear and actually be largely empty for a large body of citizenry, who will possess these freedoms legally but be unable to exercise them practically.
J. Locke, Second Treatise of Civil Government, 1689, ch. V, §§ 27, 31 :
J. Locke, A Letter Concerning Toleration, 1689 : https://socialsciences.mcmaster.ca/econ/ugcm/3ll3/locke/toleration.pdf
J.S. Mill, Principles of Political Economy, 1848/1871, esp. Bk IV : https://www.gutenberg.org/files/30107/30107-pdf.pdf
J.S. Mill, On Liberty, 1859 : https://www.gutenberg.org/files/34901/34901-h/34901-h.htm.
J.S. Mill, Chapters on Socialism, posth. 1879 :https://www.laits.utexas.edu/poltheory/jsmill/cos/cos.c01.html
L.T. Hobhouse, Liberalism, 1911, ISBN 10: 1514325276 / ISBN 13: 9781514325278
Published by Createspace, 2015.
Andrew Levine, Arguing for Socialism: Theoretical Considerations: Revised Edition, ISBN 10: 0860919188 / ISBN 13: 9780860919186
Published by Verso, 1988.
W.H. Greenleaf, The British Political Tradition, II : The Ideological Heritage. ISBN 10: 0415007100 / ISBN 13: 9780415007108
Published by Routledge, 1988.
Bernard Crick, Socialism (Concepts in the Social Sciences), ISBN 10: 0335153879 / ISBN 13: 9780335153879
Published by Open University Press, 1987.
George Blazyca, Planning is good for you: The case for popular control (Arguments for socialism), ISBN 10: 0861045068 / ISBN 13: 9780861045068
Published by Pluto, 1983.
The literature is so vast, I must settle for a small sample.