Buttons on the Lightning page are 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 the (classic) page layout anymore.
Dynamic actions can be enabled for each Lightning Page, not the whole Lightning Page, 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 clicking "Upgrade Now", you will be presented with options to Migrate or Start from Scratch.
Once this is done, any changes on the button in the "Salesforce Mobile and Lightning Experience Actions" page layout and compact layout will not impact to buttons on the Lightning page.
With Dynamic Actions enabled, you can set the action/button visibility based on criteria of the record fields, login user, or devices.