and wired up the GFCI in the same way.
Meaning 2 wires to 2 screws per side.
A GFCI is a very different kind of device that requires very different wiring. So that's why that didn't work.
You should never, ever remove the warning tape or use the LOAD terminals unless you're specifically planning to confer GFCI protection to a downline load. There is no other use for LOAD. If you only want GFCI protection at this receptacle, don't use LOAD.
And "don't use LOAD" is the configuration I recommend for novices. *
Fortunately, almost all GFCIs allow "Screw-and-clamp" attachment of 2 wires to each screw. So you should either pigtail or use the Screw-and-clamp method to attach all wires to the appropriate LINE terminal. And put the warning tape back on LOAD.
This is a particular problem with "shared neutral" or "MWBC" type circuits. LOAD cannot be used on these (not even by experts). In fact, Code requires neutrals be pigtailed anyway, so there should only be 1 neutral wire going to the recep, not 3.
* Don't get me wrong, it's clever to artfully use the LOAD terminals so you only need to use 1 GFCI per circuit, but I am very against tricking novices into doing this unawares. I'd much rather novices install 1 GFCI per recep. Doing it unawares creates huge problems, either immediately when it exposes crossed-neutral problems that the novice is totally unequipped to resolve, or down the road when something trips and they don't know how to reset it. Either way, the novice never solves the problem and rips out the GFCI, and now you're worse off.