I have a Modulus FU4, StingRay 4H non-Special, StingRay 5H Special, and a Fender Ultra Jazz. I have others, but these are in the ballpark of what you’re looking at. Just my thoughts…
The Modulus has a very unique sound due to the carbon fiber neck. It’s an exceptional instrument, but it’s a bit of a one trick pony. If you have any interest in playing music besides RHCP, then I’d consider something else. It’s not that the Modulus can’t fit in other styles, but the bass does the Flea thing (circa Californication and By the Way) exceptionally well.
The non-Special StingRay also does the Flea thing very well, but there’s a bit more to unlock via the preamp. Roll off the treble, boost the bass, set the mids to taste, and you can get some nice blues or even reggae tones. Boost the mids and treble, cut the mids a hair, and it’s funk central. It doesn’t have to specifically be a 90’s Stingray, but it should be a 3-band non-Special, IMO.
The Special StingRay is more similar to the Retro 70’s and the older 2-band StingRay (could be either Ernie Ball or pre-EB era). They have a more mellow tone and don’t do the Flea thing as easily. They’re better situated to do pop, blues, old school funk, and other softer things. Their treble EQ just doesn’t have the same sizzle and grit as the non-Specials. Again, IMO.
The Fender Ultra Jazz, thanks to its preamp, can do both modern RHCP stuff (Stadium Arcadium and newer) as well as older stuff. It isn’t a StingRay or Modulus, but the preamp allows it to get aggressive and growly in all the right ways. A regular Fender Jazz or even a Flea Jazz can get you some of the more modern Flea tones, but the lack of preamp could make certain songs feel like they’re lacking something.
The Wal is just silliness to consider. Amazing instruments, but unless you have some seriously deep pockets they are a collectors bass. You’re not going to gig one unless you’re playing the biggest stadiums simply due to how expensive they are.
So which should you get? I’d recommend going to a guitar shop and trying both a MusicMan (could be a Sterling by MusicMan) and a Fender Jazz (could be a Squier, MIM, or MIA). The main thing to look for is which is the most comfortable in your hands. The MusicMan neck is more similar to a P bass in that it’s a little chunkier. The Jazz, by comparison, is a bit slimmer. You might not favor one immediately, or you might immediately discover one is much more comfortable than the other. Sound-wise, they do different things but either will get you where you’re going with decent enough overlap. Just figure out which you’d prefer playing on and go for that one. You’ll end up getting the other at some point down the line anyways