update

If you were running macOS 10.13 High Sierra, then you can certainly run the latest officially supported versions of macOS which would be macOS 10.15.7 Catalina for an Early-2013 model, or macOS 11.x Big Sur for a Late-2013 model. While the latest version of some third party apps may not be compatible with either of these operating systems, there are still some which will work fine.

You can find the official macOS installers here:

How to download and install macOS - Apple Support

You can try booting into Internet Recovery Mode using Command + Option + R to attempt to access the latest officially supported & compatible online macOS installer for your specific Mac. Unfortunately some Macs may only boot to the online installer for the version of macOS which originally shipped with the Mac from the factory, but with your hacks.....who knows what you will happen. I believe you will first need to at the very least perform a PRAM Reset to clear the special boot parameters associated with the hack.

Or you can create a bootable macOS USB installer.

Create a bootable installer for macOS - Apple Support

Once macOS is no longer working for you on this older laptop, you could try installing Linux Mint on it which will give you access to the latest versions of the popular web browsers and LibreOffice which is a free open source office suite like MS Office. There are also a lot of other free open source apps available in the Linux Mint software repository. Linux is a great option to extend the useful life of older computers, but it does require you to learn a new OS. However, Linux is not for everyone. You can see a demo of Linux Mint by selecting the "Live" option when booting the Linux Mint USB installer. Just make sure you first make a bootable macOS USB installer now while you still can just in case the Internet Recovery Mode installer has problems. And make sure to place any important files on external media which can be accessed by any device so that Linux Mint can access those files as well. Linux Mint should work well on a 2013 Mac, just make sure you prepare in advance in case you want/need to revert to macOS again.

But we CAN help you return to High Sierra or Mojave.

if your drive will not show up to install Yosemite, this is likely because you crossed over the boundary out of the older HFS+ Extended into Apple File system (APFS), first available in MacOS 10.13 High Sierra.

You could use an external drive to install and boot Yosemite, provided it is formatted HFS+ extended.

Next:

Apply all software updates to Yosemite, available through the built-in software update mechanism. This will provide Safari 9, in addition to other improvements. Safari 9 is the oldest version that can do proper httpS;// encryption.

Then you can download and install 10.11 El Capitan or a later version, until you get to 10.13 High Sierra.

The next version, MacOS 10.14 Mojave, will convert the boot drive to APFS as it installs.

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MacOS never installs OLDER macOS over NEWER MacOS. So you will need to ERASE your Internal drive to install ANY older version directly.if you do not have backups of your files, there may be some complex ways to make them before ERASE.

The 2013 MBP is unsupported and doesn't qualify to run any macOS newer than 11 Big Sur.

Any hack that you may have used to install something newer is a violation of Apple licensing.

We cannot discuss your issues here in the Community.

2013 MBP nie jest obsługiwany i nie kwalifikuje się do uruchamiania żadnego macOS nowszego niż 11 Big Sur.

Każdy hack, którego mogłeś użyć do zainstalowania czegoś nowszego, jest naruszeniem licencji Apple.

Nie możemy omawiać twoich problemów tutaj w Społeczności.

Apple does not support those patching systems, and there are no patches the currently work beyond Sequoia. You upgraded off the end of the patches.

We can NOT help you with those patching system.

auto-translate from Polish:

Update I had a MacBookPro 13 from 2013 from one time, on which the HiSierra system was installed, and it all worked quite nicely, until the end of support.... so after applying the patches, I switched to the next system, which is Sequoia. And I can't say that although for such an old device it was a bit burdensome, but all the programs worked relatively stably..... yes, they worked- and I'm speaking in the past tense because

about two weeks ago there was an update of the system, which disabled the patch and bricked up the entire Mac..... drama..... the device moves until the login screen and that's it, the trackpad and keyboard drivers don't load, no external device connected via USB works...... anticipating questions... Yes, the trackpad and keyboard worked at 100%. I know from this reason that at the moment I am in the process of downloading the system again from the apple website.... And then YOSEMITE came !!! Another drama. The whole path from the beginning...