But does it sounds more classic or more modern?! Assuming I have a bass with maple fingerboard, can the P-46 sound like the videos I posted in the first post? thank you
In short, yes, it can sound like that, at least on my bass. Ash body, maple/maple neck. I also minimized the loading throughout, using just one 500KOhm tone pot, and a low capacitance cable. In fact, it's almost too bright like that, but I can load it with caps or turn the tone down. With stainless strings it just works perfectly for what I want it to do. You can get it to sound even more "modern" if you run it in parallel (+turn up the amp) and use loading caps to tune the sound to taste.
To me, this is THE modern P pickup, tho I suppose a "modern P" is an oxymoron

I'm not 100% sure what
modern is... Hi-fi? I wouldn't worry about Alnico 3 magnets, if they are indeed Alnico 3 (I thought they were Alnico 2)? Either way, from what I can tell, different Alnico magnets only slightly change the tone, all else being equal. But Bill designed this, so nothing else is equal - there are 5 long magnet rods per pickup half, and the coils are wound taller than most P pickups.
From my experience trying other "modern" P pickups, like DiMarzio Model P or G&L MFD, I don't find the tones I like. Too beefy sounding, IMO/IME, they don't have the right balance. I can see how they're great rock pickups, and maybe they were modern in the 70s and 80s, but they didn't work for me as well as the Wilde did. I hate to generalize from limited experience, but I've come to a conclusion that I dislike steel poles with ceramic magnets at the bottom. My sense is perhaps that steel adds to inductance, and "blunts" the edge. I think thin blade pickups might work better for that? Or pickups wound around ceramic bar magnets (no steel), but I'm not sure who makes such P pickups?
Last, I'll mention two other designs that might do the "modern P" well. First are pickups with large alnico poles, like the Musicman Caprice/Cutlass. While I didn't get to A/B them, I did try one of these MM basses in a store and liked it overall. But large poles are only the most obvious and visible characteristics, I have no idea how they are wound, and how other similar pickups are constructed. The other potentially promising design is the Nordstrand P pickup with angled poles. I only tried their Big Split and it's a mean pickup, so I presume their P pickup may be similar (maybe they'd make a custom Big Split in P housing?).
Also, this is just my opinion and experience, with all my biases. As per usual, it all depends on the particular pieces of equipment you use. My Wilde P46 sounds quite a bit different in my other P bass, which I suppose shows that it does not impart its own tone but translates well the tones that are in the bass (and bass player).