No functions deployed when deploying repo

No, Netlify just doesn’t provide the kind of runtime node.js type hosting necessary for you to host that file.

See:

You don’t need to host your own server on Netlify, all your static files are deployed to and served automatically from the CDN.

If you want to provide convenience routes for your Netlify functions you would do that with rewrites & proxies.

For example this

const searchRouter = require("./client/netlify/functions/search");
const rankedRouter = require("./client/netlify/functions/ranked");
const historyRouter = require("./client/netlify/functions/history");
const matchRouter = require("./client/netlify/functions/match");
const leaderboardRouter = require("./client/netlify/functions/leaderboard");
const championMasteryRouter = require("./client/netlify/functions/championMastery");

app.use("/search", searchRouter);
app.use("/ranked", rankedRouter);
app.use("/history", historyRouter);
app.use("/match", matchRouter);
app.use("/leaderboard", leaderboardRouter);
app.use("/champion-mastery", championMasteryRouter);

Could be in a _redirects as something like:

/search  /.netlify/functions/search  200
/ranked  /.netlify/functions/ranked  200
/history  /.netlify/functions/history  200
/match  /.netlify/functions/match  200
/leaderboard  /.netlify/functions/leaderboard  200
/champion-master  /.netlify/functions/championMastery  200

As functions automatically deploy to /.netlify/functions/filenamehere