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Fix small issues in Serve mode. #596

Job	Run time
pip-audit (dependency CVEs) (ubuntu-latest)	16s
Tests (py3.12 on ubuntu-latest)	1m 29s
pip-audit (dependency CVEs) (windows-latest)	48s
Tests (py3.11 on ubuntu-latest)	1m 29s
Tests (py3.13 on ubuntu-latest)	1m 27s
Tests (py3.11 on windows-latest)	3m 29s
Pyright (macos-latest)	20s
Tests (py3.12 on windows-latest)	3m 25s
Tests (py3.11 on macos-latest)	2m 28s
Ruff (lint + format) (ubuntu-latest)	19s
Tests (py3.13 on macos-latest)	2m 29s
Ruff (lint + format) (windows-latest)	1m 8s
Tests (py3.12 on macos-latest)	2m 20s
Tests (py3.13 on windows-latest)	3m 34s
Ruff (lint + format) (macos-latest)	26s
Build wheel, install & CLI smoke test (ubuntu-latest)	20s
Pyright (windows-latest)	1m 11s
pip-audit (dependency CVEs) (macos-latest)	20s
Build wheel, install & CLI smoke test (windows-latest)	53s
Build wheel, install & CLI smoke test (macos-latest)	25s
Pyright (ubuntu-latest)	32s
	29m 8s