Buttons on the Lightning page is set in the Classic page layout under the "Salesforce Mobile and Lightning Experience Actions" section.
Since Summer ’20 release, Salesforce introduce Dynamic Actions, with this, you can configure buttons on your record page directly within the Lightning App Builder, and will not depends on (classic) page layout anymore.
Dynamic actions can be enabled for each Lightning Pages, not the whole Lightning Pages, so you can take time just to enable the ones needed.
From the Lightning App Builder, click Highlights Panel at the top, then click the "Upgrade Now" button.
Once enabled, you cannot disable it back, unless you create the new Lightning Page for that object, or delete and add a new Highlights Panel component.
After click "Upgrade Now", you will be presented with options to Migrate or Start from Scratch.
Once this is done, any changes on the button in "Salesforce Mobile and Lightning Experience Actions" will not impact to buttons on the Lightning page.
With Dynamic Action, you can set the visibility based on criteria of the record fields, login user, or devices.