As I've stopped using this extension myself a while ago and currently have hardly time to spare, it would be nice if someone else could do the reverse-engineering part. I'd happily update the api calls and push a new version once that's done.
<?xml version="1.0" encoding="UTF-8"?>
<gupdate
xmlns="http://www.google.com/update2/response" protocol="2.0" server="prod">
<daystart elapsed_days="4663" elapsed_seconds="48885"/>
<app appid="klbibkeccnjlkjkiokjodocebajanakg" cohort="" cohortname="" status="ok">
<updatecheck
codebase="https://clients2.googleusercontent.com/crx/blobs/QgAAAC6zw0qH2DJtnXe8Z7rUJP2HvPGsVbNocCmvAYPMRjisorNmqhpnTLF5kfM_x5cjrac1ZvHxGOLo21Olggkw2LJ7BwtZ42flI_pnI31sOOUpAMZSmuUe58K32zpo3MVYzpqHgPeyd42LRQ/extension_7_1_0_0.crx"
fp="1.dc8b9ef8af7ed4d8b9d5ee658395cc034e7d00042bd7beffe6a20f897daccab3"
hash_sha256="dc8b9ef8af7ed4d8b9d5ee658395cc034e7d00042bd7beffe6a20f897daccab3"
protected="0"
size="262658"
status="ok"
version="7.1.0"
/>
</app>
</gupdate>
<?xml version="1.0" encoding="UTF-8"?>
<gupdate
xmlns="http://www.google.com/update2/response" protocol="2.0" server="prod">
<daystart elapsed_days="5215" elapsed_seconds="14970"/>
<app appid="klbibkeccnjlkjkiokjodocebajanakg" cohort="1::" cohortname="" status="ok">
<updatecheck _esbAllowlist="false" status="noupdate"/>
</app>
</gupdate>