But like I said, I’m not a political historian just an idiot with a half baked opinion.
All political movements and all politicians are convinced that their power is 100% legitimate and they should therefore be able to have 100% control of and visibility into everything that's going on.
The idea is compatible with most peoples' definition of democracy. You don't need to support other aspects of authoritarianism usually associated with right or left wing dictatorships.
As to your question: yes, most authoritarians are conservative in nature, given that the world has mostly been moving away from authoritarianism over the past few decades.
Also, I completely disagree that the world has mostly been moving away from authoritarianism. On the contrary. There was a time when at least the direction of travel seemed assured. Now I'm no longer so sure.
So please, debate policies on their content, not on their label. Reducing everything to a binary decision only serves authoritarian agendas.
But the Labour party have never been especially liberal. They're just as likely to enact controlling social policy. And, again, the press are extremely illiberal, they're likely to campaign for more surveillance.
(Don't try to jam the American two-party lens onto UK four-plus party politics, it will not help you make sense of the actual situation).
Because the UK has FPTP elections, in practice it's a two party system but which two parties varies by locale, resulting in some weird interactions that aren't really seen in the US.
You aren't going to get elaborate rainbow coalitions under that model, as you might in say Germany.
Labour are the party who passed that very nasty "Tell us your password or go to prison" law under "If you've done nothing wrong, you've got nothing to hide from law enforcement or the government." mentality.
Red Tories are still Tories.
This leaves the Lib Dems, who sadly have zero interest in repealing the Online Safety Bill if it passes.