You may need a different rear mech for the new cassette and a longer chain. Need to know what's there currentlyI'm asking, just awaiting a reply. Is the rear derailleur designed to just take up the slack when changing gears? I'm never sure about changing cassette sizes
Not necessarily, could be a short cage derailleur.
There are two variants for the RD-R3000, the GS (long cage with Max 34t) and the SS (max 32t), all of which is irrelevant because the OP is running Sora 3500 and both the SS and GS variants have a max 32t sprocket, the difference between the two is the total capacity - meaning the GS version can be used with a triple at the front and the SS can't.View attachment 460091
Shimano Sora R3000 9 Speed.
Sora R3000 9 Speed rear deailleur from shimano. Sora rear derailleur feautre a light action shifting with a wide link design give incresed rigidty for better shifting. The 11 tooth pulley wheels help to increase chain life and reduce chain noise. Available in Black compatible with 9 speed drive trains only.
Mount Direct Mount
Max Sprocket Size 34 tooth