Well, if your code can be instantiated on Julia 1.12, then you can use JETLS even if Julia 1.10 is active. So you could do:
mv Manifest.toml Manifest-v1.10.toml
juliaup add 1.12
juliaup default 1.12
julia --project -e 'using Pkg; Pkg.instantiate()'
mv Manifest.toml Manifest-v1.12.toml
juliaup default 1.10
and try if that works for you.