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Ok, got some responses from him (I don't know what any of these things mean haha):

vimtex works perfectly on neovim (in fact, the main developer uses neovim) and is very well documented

texlab (the latex lsp server) also does build and forward search (although there's a small bug at the moment)

Oh, and backward search needs neovim-remote (\o/ mhinz); just use nvr --remote +"%line" "%file" as backward search command

(the vimtex dev uses Zathura, so that may be an alternative viewer to look into)