You’re talking about making him 1:1 with his home series, yet there’s two problems with that. The first is that you’re ignoring the rest of his legacy and the second is that SRB2 is first and foremost a platformer. You can add RPG elements such as a level up or upgrade system (which we actually see working in Metroid: Vanguard) to fit his RPG upbringing, but you can’t do everything exactly the way it was in his games. Sure, hammer throw was a badge move, but how do we incorporate badges into SRB2? You suggested to replace the Emerald Tokens with badges, but now you can’t have Chaos Emeralds. There are certain liberties that you have to take when taking a character from one type of game to another.
Here’s what the ideal Paper Mario should look like when bringing in RPG Elements while also prioritizing movement. You start off with a basic move set: Jump and Hammer. Jump allows you to stomp on enemies and hammer allows you to defeat spiked enemies and destroy breakable walls. After getting a certain amount of points for defeating enemies, collecting rings, and breaking monitors, you’ll be provided with a Level Up prompt that can be opened up at anytime and lets you pick from an array of stats like jump, hammer, speed, etc., similar to the S.P.E.C.I.A.L. mechanic from the Fallout games (which are FPS games that include RPG elements because the first few games were RPG games). After picking a stat to upgrade, you’ll be provided with a new move. If you select to upgrade Jump, you could be allowed to use the Spring Jump from TTYD/Luigi’s Super Jump from SPM or fold into an airplane like in TTYD and Paper Jam. Selecting to upgrade hammer would allow you to unlock new hammers with new abilities. Taking inspiration from TOK, you can have access to hurlhammers (which would also act as the hammer throw move), the spin hammer from TTYD, the burnhammer and chillhammer, a big hammer (Could possibly use the trio hammer's design from Paper Jam) as well as all of their shiny and flashy variants. As for the Chaos Emeralds, those would act as they already do, only granting a super form and the good ending. When it comes to the health system, using either the already existing ring system or having them grant you health like in Metroid: Vanguard would be okay in my book.
tl:dr By allowing Paper Mario to get new moves that he can cycle through by using an exp system, he would be allowed to have a ton of movement options while also stay true to his origins
