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I don't think there are any services that can compare to YouTube in any way.

Technically, yes, most sites won't have such sophisticated logic. But any Google, Microsoft, or Meta service you use most definitely will.

I really liked CreepJS's "Visits" feature where it would show a counter for how many people have visited with exactly the same browser fingerprint (which would usually be 1 unless you were using Tor Browser or Mullvad Browser), but they seem to have removed it for some reason along with "Lies" and "Trust Score". You can still check it out here though to see just how much identifying information even a simple hobby project can gather in less than a second.

Try a different VPN server if you get the "Sign in to confirm you're not a bot" error. If you're using Mullvad VPN, the Netherlands Amsterdam 203 server should work.

That likely makes you easier to track. User agents don't really matter all that much if an advanced tracking script is used. When your IP address is the same, your browser engine is the same, your canvas data stays the same, your window size stays the same, your operating system stays the same, then they will just know that you also use an extension that makes your user agent not reflect your system and track you based on that too.

Use Mullvad Browser without changing anything important (change the default search engine at most) and preferably use a proper VPN to actually avoid tracking during regular internet usage. Or use LibreWolf to at least fool naive scripts.

I would suggest reading this too:
https://github.com/arkenfox/user.js/wiki/3.3-Overrides-%5BTo-RFP-or-Not%5D

Relevant links:
https://rationalwiki.org/wiki/Neoreactionary_movement
https://rationalwiki.org/wiki/Peter_Thiel