Did Catherine the Great really call for the abolition of serfdom?

This answer is based on the assumption that the OP is referring to the HBO miniseries Catherine the Great and, more specifically, the following segment of the script:

[Catherine:] But in these more enlightened times, I believe we need laws that everyone respects and obeys. The rich and the powerful, as well as the poor and dispossessed. And so something needs to change. Slavery does not have to be a Russian institution.

[CROWD MURMURS]

(speaker not indicated) That didn't go down well. I'm afraid I tried to warn your mother. All of the audience here own serfs. Most of them have thousands.

(my emphasis)

ANSWER

Catherine the Great's views vs. political reality

Catherine believed that the abolition of serfdom would have benefits and discussed reforms with her advisors. Most of them were opposed, pointing to political realities - the nobles' wealth was heavily based on the land they owned and the serfs that went along with that land. Catherine could not rule without the support of the nobles.

Consequently, her enlightened views, influenced in large part by Montesquieu's 1748 treatise The Spirit of the Laws, were not put into practice: maintaining power was more important and her actions as empress actually led to serfdom reaching its apogee:

By the second half of the eighteenth century, the rulers of the great serf states in Europe had accepted the case against serfdom and recognized, in theory at least, the need for abolition. Frederick the Great in Prussia, Empress Maria Teresa and her son, Emperor Joseph II, in the Austrian Empire, and Catherine the Great in Russia were all converts to emancipation at some future point.

The reasons for this belief that serfdom had to end at some point was that

The state had always recognized that its interests were not identical with those of the nobility and that unlimited exploitation of the peasantry harmed the fiscal, military, and economic interests of the state.

At the same time,

Catherine the Great considered herself an enlightened monarch. She toyed with the idea of curbing some of the excesses of serfdom in Russia. The reaction of the nobility to these gentle hints convinced Catherine that the security of her throne depended on dropping any attempt to interfere with serfdom. In fact, under Catherine, the serf system reached its apogee and she herself gave over a million serfs to various favorites at court.

In short, if Catherine wished to remain in power she would have to bow to the political realities of the time, namely that she needed the nobles's support to retain power and the nobles had lots of serfs. As Mark C. Wallace's comment succinctly points out,

...even an absolute monarch is going to have trouble pushing through a reform that would impoverish those who hold 90% of the wealth in society

Catherine had to come power through a coup at the expense of her husband, Peter III. The preface to Mark Cruse and Hilde Hoogenboom's translation of The Memoirs of Catherine the Great explains:

Relations with her advisers and the nobility were central to her hold on power, and Peter III and the coup had raised their expectations. Catherine’s reign has been referred to as “the golden age of the Russian nobility,” and her memoirs indicate her willingness to please those upon whom she depended.

Evidence of her views can be found in early drafts of Nakaz or the Great Instruction (published in Moscow in 1767):

Prompted partly by her experiences with Pastor Eisen, Catherine had initially been prepared to contemplate ways of ‘creating new citizens’ (that is, reducing the number of serfs), for example by allowing serfs to accumulate sufficient property to purchase their freedom. But these radical proposals were swiftly dropped after she showed drafts of her treatise to her confidants. Panin famously declared that they were ‘maxims to bring down walls’.

Source: Simon Dixon, 'Catherine the Great'(2010)

Even Alexander Stroganov was opposed:

Catherine was particularly astonished to discover that even Alexander Stroganov – ‘a gentle and very humane person’ who was ‘kind to the point of weakness’ – defended ‘the cause of slavery with fury and passion’

Further,

Vasilii Baskakov, a veteran judicial official, and Alexander Sumarokov, a conservative playwright and poet, offered detailed critiques in May 1766, as did Alexander Bibikov somewhat later. The Empress hearkened to their criticism, crossed out some passages, and rewrote others...

Source: John T. Alexander, 'Catherine the Great: Life and Legend' (1988)

Around the same time, the Free Economic Society for the Encouragement of Agriculture and Husbandry held an essay competition with the topic:

What is most useful for society – that the peasant should own land or only moveable property, and how far should his rights over the one or the other extend?

Source: Dixon

Behind this "first public discussion" of serfdom in Russia was Catherine and, among the 164 anonymous entries submitted, one was from Voltaire, with whom Catherine corresponded for many years (ref: Aaron Brick's comment). The winning entry, although critical of serfdom, made only modest suggestions for reform.

Thus, political realities were paramount and under Catherine, Russia had more serfs than ever before; she even rewarded favourites with lands and serfs (over a million of the latter). Thus, despite "the intellectual and moral case against serfdom",

in terms of practical politics, emancipation remained a utopian project.

Did Catherine really call for abolition "like Catherine the Great S01E01 (2019) shows?"

While it is well established that Catherine did hold the views expressed in the HBO episode dialogue, I can find no specific evidence for the scene as depicted. In the article HBO’s ‘Catherine the Great’: An expert’s opinion, Alexander B. Kamenskii, Professor at HSE University (Moscow) is cited thus:

Kamensky does confirm that “Catherine openly spoke for the abolition. As much is stipulated in the first draft of the ‘Nakaz’ [Catherine’s document on ‘enlightened absolutism’], and the fact of her speaking on the matter with her close circle is not at all surprising. There is plenty of evidence to support Catherine’s plans on abolishing serfdom.”

The Nakaz 1st draft and Catherine's 'close circle' are not quite the same, though, as the scene in episode 1 where the new empress is speaking to an audience of what appears to be several hundred; she had quite a number of close advisors, but not that many! Thus, Professor Kamensky's examples only confirm the content of the speech. It is unclear what exactly he means by "spoke openly", but the examples given suggest he means 'spoke openly with her (close) advisors'.