Get paged before a database runs out of available connections, not after your application starts throwing errors.
Check the database's configured connection limit, this is the number your alert threshold should be a percentage of, not an arbitrary fixed count.
Alerting at 80% of the configured maximum usually gives enough runway to investigate before connections are actually refused.
Connection exhaustion escalates fast, often within minutes, so route this alert to a channel your on-call actually watches in real time, not a digest.