[PULP-957] Error during long running synchronous upload API

Describe the bug
Trying to make a synchronous upload API with a large file (so that the request takes a lot of time) is failing with:

(pulp [c13d1db3342142918bf40e0de7757e9c]: 10.129.30.13 - - [30/Oct/2025:16:41:03 +0000] "POST /api/pulp/hyagi-s3/api/v3/content/rpm/packages/upload/ HTTP/1.0" 201 8071 "-" "curl/8.6.0" 587817)
pulp [None]: pulpcore.app.entrypoint:ERROR: Api App '1228@pulp-api-6f5cfb9878-22zn7' failed to write a heartbeat to the database.
[2025-10-30 16:41:03 +0000] [1228] [INFO] Worker exiting (pid: 1228)
[2025-10-30 16:41:04 +0000] [1] [ERROR] Worker (pid:1228) exited with code 3
[2025-10-30 16:41:04 +0000] [1264] [INFO] Worker exiting (pid: 1264)
[2025-10-30 16:41:04 +0000] [1244] [INFO] Worker exiting (pid: 1244)
[2025-10-30 16:41:04 +0000] [1240] [INFO] Worker exiting (pid: 1240)
[2025-10-30 16:41:04 +0000] [1238] [INFO] Worker exiting (pid: 1238)
[2025-10-30 16:41:08 +0000] [1] [ERROR] Shutting down: Master
[2025-10-30 16:41:08 +0000] [1] [ERROR] Reason: Worker failed to boot.

To Reproduce
Steps to reproduce the behavior:

# download a sample file
wget https://download.copr.fedorainfracloud.org/results/@dotnet-sig/dotnet-preview/fedora-41-x86_64/09584046-dotnet10.0/dotnet10.0-10.0.100~rc.1.25451.107-0.7.fc41~bootstrap.src.rpm 

# upload it using synchronous upload API
curl  https://${BASE_ADDR}/api/pulp/${DOMAIN}/api/v3/content/rpm/packages/upload/ -F file=@dotnet10.0-10.0.100~rc.1.25451.107-0.7.fc41~bootstrap.src.rpm

# alternative to make the request take longer
curl --limit-rate 5M  https://${BASE_ADDR}/api/pulp/${DOMAIN}/api/v3/content/rpm/packages/upload/ -F file=@dotnet10.0-10.0.100~rc.1.25451.107-0.7.fc41~bootstrap.src.rpm

Additional context
As a workaround, we increased the API_APP_TTL

Start with the synchronous upload API endpoint shown in the reproduction and the API_APP_TTL setting mentioned in the workaround. Review the heartbeat and worker-exit errors in the provided logs to determine how long-running uploads are handled. Done means the reproduced large or rate-limited upload completes without the API app losing its database heartbeat or shutting down.