Is it possible to install a bathroom fan, vanity power plugs, LED lights, a small towel dryer and a smart toilet on just 2 circuits?
You can share GFCI receptacles. You might have to.
OK. Here's a science fact you do not know, and neither do the people who wrote that instruction.
A GFCI is not a receptacle.   It is a system of protection that can protect any number of outlets.  In fact they make GFCIs that are not receptacles - GFCI only, or GFCI+breaker, or GFCI+switch.
Anyway, every GFCI device can protect other equipment that is wired downline of it... it has a set of terminals called &quot;Load&quot; which are for exactly that purpose and no other purpose.
Now, obviously, a GFCI receptacle protects its own sockets but it still has those &quot;Load&quot; terminals that you're not supposed to use for anything else.
So GFCIs have 4 screws - 2 Line and 2 Load.  Unfortunately, plain old receptacles have 4 screws. So when novices upgrade receptacles to GFCI, they just go &quot;la la la, 4 screws = 4 screws done!&quot;. So they are accidentally putting the downline on the &quot;Load&quot; terminals, giving it protection they don't even realize.
Those instructions are written for novices, and so they told you it needs to be a GFCI receptacle.  It does not: a plain receptacle fed from the &quot;Load&quot; terminals of an existing GFCI receptacle is perfectly fine for that requirement.
So you do not need to relocate the vanity GFCI for this purpose alone: you can simply feed off its &quot;Load&quot; terminals to grant GFCI protection to any other plain outlets in this same bathroom.
In fact, you may be required to: Code does not like GFCI receptacle in inaccessible locations, because it's too difficult to do the monthly required test.
However, the bidet requires a dedicated circuit
It's right there in the instructions, which you must follow (NEC 110.3(B)).
So that means your only wiring option is 1 circuit dedicated to the bidet, and the other circuit used for all other loads.
Bathroom receptacle circuits must be 20A
Keep in mind if this is NEW wiring, bathroom receptacle circuits must be 20A. All of them.  You cannot use a 15A MWBC (shared neutral) as a substitute (though a 20A MWBC would certainly do the trick).
If you cannot meet the &quot;accessible GFCI&quot; requirement, you can fit a GFCI deadfront (which is a device that is GFCI only) at an accessible location.
Really, the correct way to wire an outlet for a dedicated circuit is to use a 1-socket receptacle.  Those are not made in GFCI (except for GFCI+outlet+switch combo device) and so again, the deadfront might be the way to go.