I forgot the password from my minecraft account, which is why I clicked on "Forgot password". However, of course they wanted to send me an email, but my email address is no longer valid. Is there anything else I can do?
If you can no longer get hold of the email address then you have to contact support or else it will be gone
Look here:
https://help.minecraft.net/hc/en-us/articles/360035015051
You can contact Minecraft Support and show them your proof of purchase, then the account will overwrite it on your new email.
Here is the link to support:
https://help.minecraft.net/hc/en-us/requests/new