auth: improve ClientAuthenticator error messaging #2332

Job	Run time
checks / pre-commit	36s
checks / readme-snippets	10s
checks / test (3.10, lowest-direct, windows-latest)	3m 54s
checks / test (3.11, locked, windows-latest)	2m 42s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 6s
checks / test (3.14, lowest-direct, windows-latest)	2m 23s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 22s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 8s
checks / test (3.13, locked, windows-latest)	3m 13s
checks / test (3.14, locked, windows-latest)	3m 54s
checks / test (3.12, lowest-direct, windows-latest)	3m 31s
checks / test (3.13, lowest-direct, windows-latest)	8m 48s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 3s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 8s
checks / test (3.14, locked, ubuntu-latest)	2m 26s
checks / test (3.11, lowest-direct, windows-latest)	2m 45s
checks / test (3.10, locked, ubuntu-latest)	47s
checks / test (3.10, locked, windows-latest)	2m 16s
checks / test (3.12, locked, ubuntu-latest)	1m 11s
checks / test (3.13, locked, ubuntu-latest)	59s
checks / test (3.12, locked, windows-latest)	3m 24s
checks / test (3.11, locked, ubuntu-latest)	59s
all-green	5s
	49m 50s

Provide feedback