Hi Pauleduc,
Thank you for posting your questions to the Apple (user-to-user) Community.
Am no expert in this area, yet your questions certainly deserve some response.
Re: "Sound equalizer for AirPods?"
Seems the iPad's Music app has equalizer settings, although is just for that app.
If you use the Music app: See: Adjust the sound in Music on iPad - Apple Support
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Re: I would like to use my AirPods to listen to movies and other streaming content
You may be able to add your audiogram to the iPad's Health app, and you may be able to use that data in order to adjust the audio to suit your hearing needs.
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Re: " ... is there any way for me to lower the bass and increase treble on my AirPods Pro, when I am watching TV or streaming movies and series on my iPad?"
You may want to check with your hearing-specialist. Eg: An audiologist who knows your hearing needs may be able to advise / inform you.
ie: I understand there are third-party (non-Apple)) apps available that may work with equalising the audio that streams from the iPad, although I have no experience with these. They may or may not be effective for your particular needs.
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Re: "will my hearing profile be applied to these new AirPods and compensate for my hearing loss, boosting the high frequencies when I watch content on my iPads?"
As Apple users, like yourself, we can not anticipate whether the new features will be helpful to your hearing ability, or not. That is: Unless some-one with similar needs who has tried the new features shares their experience with you here.
You can check which, if any, of the features are available in your country or region:
See: AirPods Pro 2 - Hearing Health Feature Availability - Apple
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Apple support has some articles about the new features online (links below)
NB: Says for a "perceived mild to moderate hearing loss"
How to: Use hearing health features with AirPods Pro 2
More info: article says "you can take a Hearing Test with your AirPods Pro 2, or you can use an existing hearing test result (for example, an audiogram from your hearing healthcare professional ...)"
See how to: Use the Hearing Aid feature on your AirPods Pro 2
and
How to: Use Hearing Protection with your AirPods Pro 2 - Apple Support
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Apple's "Hearing health" website: info.
(NB: says: "Feature is only available in the U.S. and Canada").
AirPods Pro 2 - Hearing Health - Apple
and
How to: Use hearing health features in Health on iPad - Apple Support
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Other AirPods audio features:
How to: Use Adaptive Audio your AirPods - Apple Support
You can: Set headphone accommodations for AirPods - Apple Support
All the best :-)