Why does Polish use W instead of V?
since almost all other Slavic languages use V?
Polish orthography has been evolving for centuries and always stayed very conservative. There had not been any major changes since late 16th century (although some changes, especially regarding rules for letters i, y, j, occured a few times) in it. And the letter w is a remnant from those times.
It’s been indeed borrowed from German writing tradition, but it could be found in earlier Czech texts too (I believe there were some with w in late 19th c.).
Most modern Slavic orthographies utilising Latin script were developed in late 19th/early 20th centuries, and thus adapted letter v for that sound. But Polish, because it had a long writing tradition with that orthography, which stayed nearly unchaged, never did the switch.
Same is true for sz, cz, and rz, those once were also possible to be found in Czech texts, alongside zz. When Czechs came up with š, č, ř, ž, every Baltic and Slavic language borrowed those, except Polish, which uses only ż (earlier version of ž) because zz was problematic. Even biełaruskaja łacinka (Belorusian Latin script) uses now š and č, even though it has been created on the basis of Polish orthography.
From what I've read, it actually comes from Germanic languages, which used the "vv"(double v) ligature to represent a sound similar, but different to the latin /v/. Poles probably also used a consonant which was much closer to the germanic equivalent, rather than the latin one, and that's why "w" became more widespread, and it just stayed that way.
Still, I'm no expert, so don't take my word for it.
Yes, it does seem polish is quite influenced by Germanic languages, so this doesn't surprise me.
It might have nothing to do with the reason, but I do find "w" easier to write (than "v") in a distinct way. It just quick double "u"s, whereas with "v" you need to make a sharp bottom end, or it would look like "u".
Note that since my native is Polish, letter "v" isn't my native either. Maybe I'm just not that used to it.
I write my w's a two Vs. So my handwriting looks like vv rather than w. V is much easier to write than w for me haha.