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I share a similar setup and facing the exact same problem.
Here is a snippet from the log.
Detected the following buildpacks suitable to build your app:
[2022-11-17 16:14:03] │
[2022-11-17 16:14:03] │ heroku/nodejs-engine v0.5.1
[2022-11-17 16:14:03] │ digitalocean/node v0.3.4 (Node.js)
[2022-11-17 16:14:03] │ digitalocean/procfile v0.0.3 (Procfile)
[2022-11-17 16:14:03] │ digitalocean/custom v0.1.1 (Custom Build Command)
[2022-11-17 16:14:03] │
[2022-11-17 16:14:03] │ For documentation on the buildpacks used to build your app, please see:
[2022-11-17 16:14:03] │
[2022-11-17 16:14:03] │ Node.js v0.3.4 https://do.co/apps-buildpack-node
[2022-11-17 16:14:03] ╰─────────────────────────────────────────────╼
[2022-11-17 16:14:03]
[2022-11-17 16:14:03] ╭──────────── build caching ───────────╼
[2022-11-17 16:14:03] │ › checking for cache from a previous build
[2022-11-17 16:14:05] │ Restoring metadata for "heroku/nodejs-engine:nodejs" from app image
[2022-11-17 16:14:05] │ Restoring metadata for "heroku/nodejs-engine:yarn" from app image
[2022-11-17 16:14:05] │ Restoring metadata for "heroku/nodejs-engine:toolbox" from cache
[2022-11-17 16:14:05] │ Restoring metadata for "digitalocean/node:node_modules" from cache
[2022-11-17 16:14:06] │ Restoring data for "heroku/nodejs-engine:nodejs" from cache
[2022-11-17 16:14:06] │ Restoring data for "heroku/nodejs-engine:toolbox" from cache
[2022-11-17 16:14:06] │ Restoring data for "heroku/nodejs-engine:yarn" from cache
[2022-11-17 16:14:06] │ Restoring data for "digitalocean/node:node_modules" from cache
[2022-11-17 16:14:16] ╰───────────────────────────────────────╼
[2022-11-17 16:14:16]
[2022-11-17 16:14:16] ╭──────────── app build ───────────╼
[2022-11-17 16:14:16] │ ---> Node.js Buildpack
[2022-11-17 16:14:16] │ ---> Installing toolbox
[2022-11-17 16:14:16] │ ---> Getting Node version
[2022-11-17 16:14:16] │ ---> Resolving Node version
[2022-11-17 16:14:17] │ ---> Reusing Node v16.16.0
[2022-11-17 16:14:17] │ ---> Parsing package.json
[2022-11-17 16:14:18] │ ---> Installing yarn@1.22.19
[2022-11-17 16:14:20] │ ---> No file to start server
[2022-11-17 16:14:20] │ ---> either use 'docker run' to start container or add index.js or server.js
[2022-11-17 16:14:20] │ Project contains yarn.lock, using yarn
[2022-11-17 16:14:20] │ Reusing cached node_modules from yarn.lock
[2022-11-17 16:14:23] │ Running custom build command: yarn build --filter=api
[2022-11-17 16:14:24] │ yarn run v1.22.19
[2022-11-17 16:14:24] │ $ turbo build --filter=api
[2022-11-17 16:14:24] │ • Packages in scope: api
[2022-11-17 16:14:24] │ • Running build in 1 packages
[2022-11-17 16:14:24] │ • Remote caching disabled
[2022-11-17 16:14:24] │ api:build: cache miss, executing ac8bc1e9485e9786
[2022-11-17 16:14:25] │ api:build: $ rimraf dist
[2022-11-17 16:14:25] │ api:build: $ nest build
[2022-11-17 16:14:29] │ api:build: src/activities/activities.controller.ts:11:8 - error TS2307: Cannot find module '@nestjs/common' or its corresponding type declarations.
[2022-11-17 16:14:29] │ api:build:
[2022-11-17 16:14:29] │ api:build: 11 } from '@nestjs/common';
[2022-11-17 16:14:29] │ api:build: ~~~~~~~~~~~~~~~~
[2022-11-17 16:14:29] │ api:build: