Don't grout corners. Caulk smoothed over with a tool and that gap will disappear

This was my first idea! Im too concerned with putting any type of load on the existing drywall and the joist configuration will make it difficult, but i could hand something, right? I even bought some light molding to frame it to hide the edges. How would you start?

This is correct and use masking tape to keep straight lines on both sides while using a tool or card stock to make the caulk look super smooth without lumps or edges.

Thanks. I think you're right but was hoping this wasnt the case

Thankfully they arent too crazy expensive. Home Depot sells aluminum ones, more durable than the old wood. They also have pistons to move with the ladder when unfolding or folding. Wayyyyy safer than the springs. I had an old metal spring explode on the ladder in my garage. Not good.

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Are all of the rim jets working? We had some of ours partially plugged with calcium build up and would drip after the toilet was filled.

This is with the supply shut off?

I don't really see that you have a choice. The patch as-is doesn't have enough support, you either need to support it or replace more of the old drywall until you get back to studs

If it was cracked, wouldn’t the dyed water currently in the tank be visible in the clear water of the bowl?

Put in an access panel

based on what you've said here I'd check to confirm the overflow tube isn't cracked. As you've removed the rim holes (bowl wash) hose AND water still is continually draining then logic dictates the pipe that separates the tank from the rim holes is cracked.

This makes sense. I hadn't thought of this.

If all 4 sides of your patch are supported, you are good to go. Use setting mud, and fiberglass tape for your first coat.

Go to your local lumber yard and buy a piece of 1"x3". Cut pieces to fit the long edges and place them with 50% overlap above the existing drywall. Screw each piece in using drywall screws. Install your filler piece, I would suggest to place the screws about 6-8" apart. Use dry mix compound (Sheetrock/Durabond) for the first coat. https://www.homedepot.ca/product/saint-gobain-adfors-250-ft-fibafuse-drywall-tape/1000754764 Fibafuse is premium drywall tape and is better for butt joints. 2nd & 3rd coats can be premixed mud if you wish as it sands easier. Good luck.

Put a little piece of wood above on the 4 corners, half way behind the old and halfway out where the new will attach. Run screws into the wood through the old board (hold it down above so it won't raise up with the screws), then put the new piece back up add screws to those 4 corners and to all the places you have them now - and you're good to go.

Nope, have recently replaced both bolts and neither has any evidence of water. It’s almost if somehow water from source is bypassing the tank and going straight to the bowl jets.

The old drywall crumbled las time a drill touched it, which is why I am a little nervous affixing anything to it.

I think what was meant was to pull the drywall patch and take a 2x4 cut to length on each side sistered to the framing that's already there. You then screw the drywall into that sistered wood to support the patch. Basically you are trying to make the new drywall piece as strong as the full sheet by screwing it to the wood.

How about from the bolts that hold the tank to the seat? I live in a place that has hard water and those end up being the leaks after a couple of years

Take out the drywall, cut some squares of plywood and fit one to each corner of the hole so it bridges between the new and old drywall. Screw it down to the old drywall, then fit the new piece and screw it in too

They in hell already, or going there yet?

There's nothing behind the edges, where you see screws are where the joists are

Start talking in details. What’s the size of the cut out. Where are your nearest joices in inches. This will Allow detailed accurate responses here.

I’m hoping that’s the issue, it’s just crazy it’s taking this long to drain out after a flush from 18+ hours ago.