SPAs deployed to Netlify need a special redirect as mentioned in the History pushstate and single-page apps documentation.
Better to have a specific rewrite for the backend for example
[[redirects]]
from = "/api/*"
to = "https://api.somewhere.com/v1/:splat"
status = 200
[[redirects]]
from = "/*"
to = "/index.html"
status = 200
where all requests to the /api path are routed to the backend. You can read a more detailed post here.