Hi there,
The classic P2 theme has not been tested with the block editor, so it is likely that it is missing the full compatibility that is needed for blocks. This classic version of the theme is not in active development so there are no plans to add full compatibility with Gutenberg.
The new version of P2 requires WordPress.com hosting in order to power it’s more advanced feature set, so it is 100% compatible with blocks, but there is not a “self-hosted” version that is available: https://wordpress.com/p2/
Since you want to self-host you may wish to try the P2 Breathe theme (downloadable from Github) along with the O2 plugin (also available from Github) as that is the “2.0” version of P2, but please note that this version is also not in active development (it has been replaced by the WordPress.com-hosted solution I linked above) so it is offered without support.
Hope this helps point you in the right direction!
