How do I make my Mac boot from an external SSD instead of the internal HDD?

have you gone to Apple Menu > System Settings > General > Startup Disk and select your external drive as the one you want to boot into?

Why it’s slow: Why is my hard disk drive iMac so slow? - Apple Community

How to boot external: Use an external SSD as your startup disk … - Apple Community

In that latter link, go through the “finish up” section.

What is the exact model of your iMac & version of macOS? You can get this information by clicking the Apple menu & selecting "About This Mac".

I have seen macOS begin to boot an external drive, then suddenly switch to the internal boot drive when something unexpected happens while booting the external drive. It is very frustrating since macOS provides no notice of it happening or any error messages. I need to do a bit of research to see if I can find a way to gather some clues on what is occurring during that boot process.

In the mean time you can try the following:

Run Disk Utility First Aid on the hidden Container of your external SSD (assuming you are using macOS 10.13+). Within Disk Utility you may need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. Even if the First Aid summary says everything is "Ok", click "Show Details" and scroll through the report to see if there are any unfixed errors or warnings. If there are errors/warnings, then run First Aid again until they are gone. If after several scans, the errors remain, then try running First Aid while booted from Recovery Mode. If after several scans in Recovery Mode the errors remain, then you will need to perform a clean install of macOS which involves first erasing the SSD followed by reinstalling macOS & restoring from a backup.

Run the third party app EtreCheck and post the complete report here so we can examine it for possible clues.

How to use the Add Text Feature When Posting an EtreCheck Report - Apple Community

Run the third party app DriveDx (free trial period) to check the health of the internal drive(s) and even the external SSD. To check the health of the external SSD will require installing a special USB driver. If you can still boot to the internal drive, then I would suggest running DriveDX while booted to the internal drive.....this way you don't have to have the third party driver on your main external boot drive which you use every day (choice is yours). Post the complete DriveDx text reports for each drive here by using the "Additional Text" icon which looks like a piece of paper on the forum editing toolbar. I will review the DriveDx reports. If the internal drive(s) are still healthy, then I have an option that may help ease this situation, but it would be nice if we can figure out why this is occurring since it indicates some sort of problem.

FYI, make sure to run EtreCheck while booted to your external drive so we gather logs & details from the external drive.

Disconnect all other external devices (except mouse & keyboard) just in case one of them is causing a problem. Make sure the external SSD is connected directly to the iMac.

ok. my next suggestion, have you tried to attach the external drive to a different port on the Mac? (if you have one) or a different cable? although I'm uncertain that would help as you can "option boot" into that drive.

Try a PRAM Reset (hold for at least two chimes if possible). Afterwards you will need to reconfigure the default Startup Disk again since the reset wipes out those settings. Maybe the PRAM is corrupted & this can fix it.

Edit: The keys you listed were incorrect.....the Control key is not used, it should be the Option key.