Am checking the App Store using MacOS 13.7.8:
At the top of the "Logic Pro" page it states: "Requires macOS 14.4 or later"
Yet if I click on "Version History" There's a long list of updates from 10.5.1 to 11.2.2
Seems the App Store will download the newest compatible app for your currently installed MacOS. As long as Logic Pro is in your purchase history, App Store should not charge you.
Thanks to yoyoBen for joining the discussion, and sharing that manual method.
Seems you will see the "open" button as long as the old version remains in use.
Temporarily moving Logic Pro to the trash may now show you the option to get / update / download. (The trashed version can always be restored if need be.)
Apple support's tips: Redownload apps and games from Apple - Apple Support
or
If there’s an issue when you redownload apps, movies, or other content from Apple - Apple Support
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Else: If more help is needed: You might want to contact the Billing and Subscriptions support Team, who handle App Store purchases and problems: (online chat, phone, email etc.) There's a "Get Support-start now" link at the Bottom of their web-site: Subscriptions and Billing - Official Apple Support