Hi, and welcome to the Apple (user-to-user) Community!
Re: "iPhone auto brightness :While thinking over the crossword puzzle the screen dims."
Seems you may have added an app that runs constantly in the background, always using power ?
You may also have low-power mode on so that the iPhone uses less power, charges less often.
If so, you may want to turn low-power mode off, and / or turn off the app you installed, when you want the screen to stay bright longer.
Apple support's online article: Use Low Power Mode - Apple Support : says:
"Low Power Mode reduces the amount of power that your iPhone or iPad uses when the battery gets low.
To turn Low Power Mode on or off, go to Settings > Battery.
You can also turn Low Power Mode on and off from Control Center. Go to Settings > Control Center > Customize Controls, then select Low Power Mode to add it to Control Center."
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Else: You may want to check through this discussion thread on a similar dimming topic.
ie: Some of the suggestions given by other users may be worth trying out.
iphone 13 pro max screen dimming - Apple Community
or
See how to: Adjust the screen brightness and color on iPhone - Apple Support
All the best :-)