How can I run Mojave VM in Catalina

Before you contemplate a Virtual Machine on your Mac, it should have 16 GB RAM or better with emphasis on better. You should expect the fans to run as Virtual Machines running concurrently with the operating system generate more heat and slurp battery. Consider doing so plugged into a power supply.

Parallels Desktop Pro will run you at least $120/yr subscription — I know because I use it. And although VMware used to offer a free Fusion app for non-commercial users, there is no telling what the monetizing Qualcomm as new owners will do about that freebie in the future.

Either VM would allow you to run Mojave as a guest operating system on Catalina. I am running Mojave as a guest on Monterey using Parallels and it works fine. I also happen to have a 3.8 GHz Core i7 with 40 GB ram. Parallels can use the macOS App installer as it source to create the guest. Once one has the Mojave operating system installed as a fresh guest, one can reconfigure Parallels so that you can boot Mojave into Recovery, and Restore from a Mojave Time Machine backup so your original Mojave installation is present as a guest.

Then there is the free Oracle VirtualBox which is substantially behind in the Virtual Machine offerings, even if it is free. They only officially support the server versions of OS X Leopard, or Snow Leopard as guests, and any other macOS guest is purely experimental and lagging in performance.

I purchased a fast external SSD (Crucial X8 1TB) to store all of my Virtual Machine guests on, and plug that USB-C cable from the drive into the ThunderBolt 3 port on my 2020 iMac.

SunshineAnderson wrote:

But my iPhone, running IOS 14.4.1 syncs with my my MacBook so I can't update it or it will stop syncing,

Not sure where you get this from, but your iPhone should continue to sync with Mojave. I may request a small firmware update some times, but that is just a firmware update, not a complete OS version update.

Can I run both using Parallels or similar and what is the best sequence

of operations to load both. I have Time Machine backups on separate HDs

Yes. You can run Mojave in a virtual machine through Parallels if you want to, or even as a side OS on a dedicated partition or an external drive if you really wanted.

You can update to Catalina first, and then install a compatible version of Parallels on it, an then install Mojave in a virtual machine on it.

It might probably be better to install it separately rather than through parallels, so it gets all the Macs resources, rather than sharing them with Catalina though.

In fact, I would install Catalina on an external drive first to verify all compatibility first before upgrading the main system to it.