integrations: Remove deprecated !avatar syntax from git integration #632

Job	Run time
Debian 12 (Python 3.11, backend + documentation) (Zulip refs/tags/7.0)	5m 59s
Ubuntu 22.04 (Python 3.10, backend) (Zulip refs/pull/36159/head)	6m 18s
Debian 11 (Python 3.9, backend) (Zulip refs/tags/4.0)	5m 1s
Ubuntu 24.04 (Python 3.12, backend) (Zulip refs/tags/8.5)	4m 13s
	21m 31s

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