To break or not break tabs when installing an electrical outlet
With an ordinary duplex receptacle (GFCI is a bit different), there are two ways it can be installed:

Combined = tabs in place

In this mode, the two hots are connected together and the two neutrals are connected together. Both receptacles are powered from the same source. If you want to power an additional receptacle (or lights or whatever) from the same power source, you can use the second set of screws (or backstab connections, but those are not recommended) as a way to daisy-chain to the next device. Alternatively, you can also chain to another device using pigtails with a single set of hot/neutral wires &amp; screws.

Split = tabs removed

With the tabs removed, you have two totally separate receptacles. Each can be on a different circuit! Except not entirely - for safety reasons the circuits should be together, typically using a Multi-Wire Branch Circuit (MWBC). An MWBC uses two hots with one neutral - the hots each 120V compared to neutral but 240V compared to each other. In the case of an MWBC, the neutrals are actually shared, so you would not remove the neutral tab, just the hot tab (and there are other complications which mean that neutral would itself be on a pigtail even if only one other device is connected).
There is another use for removing the tabs - a half-switched receptacle. With this configuration, hot goes to one hot screw and switched hot goes to the other hot screw. Neutral still gets one wire and the tab is left in place. This lets you use a plug-in lamp with a switch while still having an always-on receptacle for other stuff. Personally, I prefer ceiling fixtures, but builders like to save every $ they can...
The end result is that the hot-side tab is removed in certain specific cases but the neutral-side tab is hardly ever removed - only realistic case I can think of is a top/bottom MWBC split on a double-breaker GFCI.
And since your original didn't have the tabs removed, the replacement doesn't either.