It does not block 1st party cookies, it just blocks the consent pop-up.
These pop-ups are used for consent for 3p cookies (3p=3rd party) and brave already blocks 3p cookies. If you remember the pop-ups, then you will know that the ‘essential cookies’ are always loaded and you do not get consent for it.
This essential cookies are what store your login for eg., twitter, youtube etc.
When you just block the pop-up, you do not give consent nor take back your consent, meaning the site just loads the essential cookies which are the useful ones.
It is very similar to when some pop-ups have the option like ‘Reject non-essential’ or ‘Accept only Essential’ in the list.
I have been using this feature in brave for 1 year and before brave for another 1 year and not a single site has broken up for me.
Comparison with Tor browser is not similar as tor browser bundle always runs in private mode where cookies are destroyed whenever the user closes the browser window.
If you do not like this feature after turning it ON, you can always turn it OFF from brave://shields/filters