Certain errors terminate process async with unhelpful error (e.g. incorrect user and/or password)

Steps to reproduce

Try connect to Neon with incorrect username and/or password

Expected result

error event listeners fire on NeonPool and the cause of the error as returned by the Neon postgres server is thrown up to the calling application code.

e.g. when using via the Prisma adaptor:

PrismaClientUnknownRequestError: 
Invalid `prisma.$executeRaw()` invocation:

Error in connector: Error querying the database: ERROR: no such user
    at Vn.handleRequestError (.../node_modules/@prisma/client/runtime/library.js:121:7530)
    at Vn.handleAndLogRequestError (.../node_modules/@prisma/client/runtime/library.js:121:6663)
    at Vn.request (.../node_modules/@prisma/client/runtime/library.js:121:6370)
    at async l (.../node_modules/@prisma/client/runtime/library.js:130:9617) {
  jse_shortmsg: 'PrismaClientUnknownRequestError: \n' +
    'Invalid `prisma.$executeRaw()` invocation:\n' +
    '\n' +
    '\n' +
    'Error in connector: Error querying the database: ERROR: no such user'

Actual result

An unhelpful error is thrown immediately, terminating the process async from the call site:

Error: Connection terminated unexpectedly
    at fn.<anonymous> (.../node_modules/@neondatabase/serverless/index.mjs:1250:44)
    at Object.onceWrapper (.../node_modules/@neondatabase/serverless/index.mjs:410:15)
    at fn.emit (.../node_modules/@neondatabase/serverless/index.mjs:397:12)
    at v.<anonymous> (.../node_modules/@neondatabase/serverless/index.mjs:1202:66)
    at v.emit (.../node_modules/@neondatabase/serverless/index.mjs:397:12)
    at WebSocket.<anonymous> (.../node_modules/@neondatabase/serverless/index.mjs:988:51)
    at [nodejs.internal.kHybridDispatch] (node:internal/event_target:816:20)
    at WebSocket.dispatchEvent (node:internal/event_target:751:26)
    at fireEvent (node:internal/deps/undici/undici:11547:14)
    at TLSSocket.onSocketClose (node:internal/deps/undici/undici:11946:7)

Reproduce the failure by connecting to Neon with incorrect credentials through NeonPool, then inspect the package's asynchronous connection and error-handling path; the reported stack points to node_modules/@neondatabase/serverless/index.mjs. Done means the error event reaches NeonPool listeners and the server's authentication error is surfaced to the calling application instead of an unhelpful asynchronous termination.