Agile is known everywhere. Most folks know the terms and activities. That is your main challenge.
What you see is not agile. but it is likely that the people involved are not ignorant about agile and terms used.
More learning is required by you.
a starting point for testers finding themselves in a new company and wanting to do Agile, but still not knowing ...
Solve a real problem using it.
Any process has value in proportion to the value it adds by solving an real problem in real team in a real project.
How would you solve a real problem in your project using agile?Think it over.
I would suggest go small.Plan small.Point at low hanging fruits and quick wins which adds substantial value as a starter to win ...
Well you'd likely start by addressing the Manifesto, and trying to get the company behind some of these principles.
And the values:
Individuals and interactions over processes and tools
Working software over comprehensive documentation
Customer collaboration over contract negotiation
Responding to change over following a plan
(valuing left over right, but ...