Shimano's "spec" for that mech is essentially 34T max rear sprocket size, but more significantly about 33T total capacity
You MIGHT be able to push a 36T rear sprocket with a longer B screw (or reversing the original one)
I know its not much over the stated max tooth spec but it seems most of the pre dynasys derailleurs (road or MTB) can realistically clear a 34T without too many issues, but thats about the max.
The big issue is likely gonna be the capacity spec (ie total tooth difference front and rear) with you're current setup. With the front triple (20T diff) and 11 to 36 cassette (25 T diff) you're sitting at around 45T which is overshooting the capacity spec for the mech by a very large margin
For sure you can size the chain so that big/big will work without it trying to pull the mech out of the hanger, but its almost certain you won't get enough tension in the smaller sprockets on the granny - maybe even on the middle ring as well - due to the cage being too short to be able to pick up the slack on that much of a tooth difference. The chain will be loose and hanging down and you'll get massive amounts of chain slap unless you're happy avoiding those combinations (which is better than the chain being too small, so that big/big causes actual damage)
Like others above I also have had some success pushing the specs a fair bit - eg I had a 5600 era 105 short cage road mech successfully changing an 11-34 at the back and a 50-34 compact double at the front - but TBH it WAS pushing it to the limit, both in terms of max sprocket size and total capacity and I ended up changing it for an M650 DX long cage which is a lot happier - better chain tension at the extremes.
With
either mech, 34T at the back was the max I was comfortable with achieving (which is 6T more than shimano's spec for the 105!) and 36T would have been too much IMO without a hanger extender like the wolf tooth road link or similar. The resultant capacity of 39T was also pretty much the limit of what was possible with the 105 short cage mech (again about 6T over spec) and still being mostly usable at the extremes - but again, there was a lot less compromise in chain tension at the extremes with the long cage DX in.