I have an sfdx project opened in VS Code as workspace folder. I don't see the option for "SFDX: Push Source to Default Scratch Org" in the command palette. Other commands like "SFDX: Refresh SObject Definitions" are visible and I can execute them just fine.
This question No Option for “SFDX:Authorize an Org” command in VS Code Command Palette does not help, since I have an sfdx project already.
In my case I am logged in a scratch org with a namespace.If I run the command
sfdx force:org:push in the command line, it gets executed just fine. And sometimes when I reopen VS Code with the same workspace folders, I can see "SFDX: Push Source to Default Scratch Org" in the command palette.