software update

sarpy11 Said:

"software update: None of them worked and I have checked for storage as well... When I press software update it sends me to app store but nothing comes up."

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Try getting it through this link: How to Get Old Versions of macOS - Apple Support

Important: Be certain to create a backup of your Mac prior to all of this. That way, you can have something to restore from the Mac from, should anything go wrong with the install. Once installed, create a second backup.

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence

One may consider upGrading to High Sierra first if considering upgrading to any version above High Sierra. This may better position the computer for the Drive Conversion to the newer APFS format as well as any EFI BOOT ROM required to use the newer file format.

Tips Big Sir Upgrade Released Nov 2020

Tips Monterey Upgrade  Released Oct 25, 2021

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation

sarpy11 Said:

"software update: I cannot see a software update in app store, even though my MacBook Pro (13-inch, 2016, Four Thunderbolt 3 Ports) is new enough to get an update"

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Three Things...

A. Use Ethernet:

On the Mac, you would connect it through Ethernet, going directly into your router. For a Mac that does not have an Ethernet port, this would be the adapter to use: Belkin USB-C to Gigabit Ethernet Adapter - Apple

B. Different Admin User:

For Troubleshooting Purposes, create a new Admin user, seeing if you can update off of that.

C. Safe Mode:

[Hold Down: the shift key upon boot]. Try installing this in Safe Mode. While in Safe Mode, login items do not open at login, certain system preferences are set aside, and damaged system files (i.e. caches) are set aside.