GFCI outlet with two branches

Absolutely yes ! you could have as many receptacles fed off this load terminal as you want! (Pig-tailing is the right way to do multiples)

Would you like 1,2,3 branch circuits going in different directions from the load? This is 100% code compliant!

Caution there are internet only electricians that do not understand both code and the use of the load terminals your use of the load for multiple loads , branches is code and device compliant.

It sounds like you (will) have 2 branches coming off the GFCI receptacle. That is fine.

For each branch, decide whether it makes sense for that branch to be GFCI-protected and you want their ground faults to trip this GFCI device... and if "yes", then that branch's hot and neutral go on the "Load" terminals.

Otherwise they go on the "Line" terminals. If you want the GFCI protection but don't want the mutual trip, those branches can be protected by their own GFCI outlets further down the line. This might be relevant to a thing like a refrigerator, where you want the least probability of a nuisance trip.

Also, sticking "GFCI Protected" labels on all downline receptacles is mandatory per Code.* If you hate those stickers, either make your own (which is fine) or don't use "Load" and protect them with their own GFCI receps if need be.

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* A vast web of Codes, including NEC (110.3B) and UL's practices in approving the instructions of GFCI receptacles. It's not just in every brand of GFCI's instructions, it's specifically 8(c) in every brand's instructions.