The messages given by Apt are not relevant here, it is not implying any issue with your installation of Miktex; there will be some other issue affecting your LaTeX compilation. Here's what they mean:
Err:5 https://ppa.launchpadcontent.net/staticfloat/julia-deps/ubuntu jammy Release
404 Not Found [IP: 185.125.190.52 443]
The PPA for providing julia-deps does not support your version of Ubuntu, it hasn't been updated for some time and may be abandoned.
You can remove it with sudo add-apt-repository -r ppa:staticfloat/julia-deps
to remove the message, or you can leave it there and the repository might add support but Ubuntu 22 one day. julia-deps is a list of packages used for compiling Julia on Ubuntu, it's not related to Miktex.
E: The repository
N: Updating from such a repository can
This is a summary of the previous error with julia-deps.
W: http://miktex.org/download/ubuntu/dists/jammy/InRelease: Key is stored in legacy trusted.gpg keyring (/etc/apt/trusted.gpg), see the DEPRECATION section in apt-key(8) for details.
This is a warning about the deprecated method of storing keys insecurely, it won't stop you updating or installing Miktex right now, to resolve the warning follow this answer
N: Skipping acquire of configured file 'universe/binary-i386/Packages' as repository 'http:
When you have the i386 architecture enabled in Apt, it will check repositories for provided i386 packages, but not all repositories support i386 anymore, so it will generate this message, it won't cause any problems here.