I would advise removing the Ubuntu Tweak PPA from your software sources by opening the Software Centre then clicking Edit->Software Sources.... Click the 'Other Software' tab then untick the Ubuntu Tweak PPA.
Close the software sources window and it should refresh your software index.
Uninstall any flash plugins you have installed then install ubuntu-restricted-extras. This should get flash working again.
In the future do not use PPAs unless you are certain of what you are doing. Note that Ubuntu Tweak is for users who know what they are doing and can mess up your system if you use it without precautions.
So, using the link provided by @wraith3690-001 I am able to answer my own question :)
According to this guide (I recommend to download it for reference before Flash EOL), the Flash player itself will block content after EOL date. To work around this, one needs to create a file /etc/adobe/mms.cfg. Right now, if you put a line EnableAllowList=1 into that file, you can basically get a simulation of what will happen after EOL date (as according to the guide, this setting will be enforced automatically after EOL). What will happen is that instead of Flash content, the Flash player displays an icon which, when clicked, leads to the Adobe Flash EOL information page.
To allow Flash content to run, you need to put in the /etc/adobe/mms.cfg file lines specifying which sites Flash player is allowed to access, in the following form:
AllowListUrlPattern=http[s]://site.domain/
If you want to specify both https and http for a site, you may put two lines for https and http, or you can use the following shortcut:
AllowListUrlPattern=*://site.domain/
You may also specify something like AllowListUrlPattern=file:/// for local files, although it looks superfluous because Firefox does not support playing local Flash files via Flash plugin anymore, and standalone Flash player (I also suggest to download it from Adobe while it's available) seems to always run file specified by command line or menu option regardless of EnableAllowList setting.
You can also put EOLUninstallDisable=1 into /etc/adobe/mms.cfg file to suppress prompts to uninstall Flash that are mentioned on the Flash EOL page.
To keep Flash software for later reinstallation there are two options:
a) the flashplugin-installer package which probably most of us use now:
The package can be downloaded from http://archive.ubuntu.com/ubuntu/pool/multiverse/f/flashplugin-nonfree/ (the current version as of this writing is flashplugin-installer_32.0.0.414ubuntu0.20.04.1_amd64.deb). However, this package contains actually (according to it's name) only the script that installs the plugin. The actual Flash software is downloaded during installation of the package from http://archive.canonical.com/pool/partner/a/adobe-flashplugin/. As of this writing, the current filename downloaded is adobe-flashplugin_20200811.1.orig.tar.gz.
If the latter won't be available for download, the installation of the package will likely fail. I suppose, however, that if you put the (previously saved) .tar.gz file into a correct directory before installing the package, the installation may succeed. However, I don't know what that correct directory is - I'm still investigating...
b) the alternative is to use adobe-flashplugin DEB package, which may be downloaded from the same location http://archive.canonical.com/pool/partner/a/adobe-flashplugin/ (current filename is adobe-flashplugin_20200811.1-0ubuntu0.20.04.1_amd64.deb). Looking at it's contents, it installs the plugin without downloading any external files.
For running local .swf files, I also strongly suggest to download the standalone Flash player from Adobe as said above.
Best Answer
Google Chrome for 64 bit does not come with Flash (see bug report). Chrome (64 bit) will try and use the Flash it finds on your system, but if you don't have it, then you need to install it.