You will need to boot to a macOS installer either through Internet Recovery Mode (Command + Option + R) to attempt to access the online Catalina installer, or you can boot from a bootable macOS USB installer (preferably Catalina). Even if you cannot boot to a Catalina installer, you can still install an older version of macOS to the external drive, then upgrade the OS on the external drive to Catalina.
Once booted to a macOS installer, you will need to launch Disk Utility. If booting to a macOS 10.13+ installer, then you will need to click "View" within Disk Utility and select "Show All Devices" before the physical drives appear on the left pane of Disk Utility. Select the external drive and erase the whole physical external drive as GUID partition and APFS (top option) if using a macOS 10.13+ installer. Otherwise if you are booting an older macOS installer such as Lion or Mountain Lion or Mavericks, or even Yosemite, then you will need to instead partition & format the whole physical external drive using the instructions in the following article (Apple changed how Disk Utility works beginning with macOS 10.11 El Capitan):
https://eshop.macsales.com/tech_center/formatting/Mac_Formatting_6-10_R3.pdf
If you are booting a macOS 10.11 El Capitan installer, then you will need to erase the whole physical external drive as GUID partition and MacOS Extended (Journaled). This should cover all the installers that you may encounter.
The main thing is making sure to erase the external drive since erasing a drive will destroy all data on it. Make sure to give it a unique name so you don't confuse it with the volume name of the internal drive. Maybe name the new volume on the external drive "ExternalOS".
Quit Disk Utility and select the "Install macOS" option. Again, make sure to select the external drive as a destination.
Sometimes when the macOS installer finishes the phase 1 copying of installer files to the external destination drive and reboots, the Mac may end up trying to boot to the internal drive. If this happens, then force a power off by holding the power button down until the system powers completely off. When you power the laptop back on, then make sure to hold the Option key immediately after hearing the startup chime. This will give you the Option boot screen or Apple boot picker menu where you will need to select the orange icon indicating the external drive. This should allow phase 2 of the OS installation to run & complete.
If you are installing anything other than Catalina to the external drive, then you should upgrade the external drive to Catalina if you want to use Disk Utility to run a First Aid scan or to attempt to access data on the internal SSD. If you do not need to do either, then you can just run DriveDx (free trial period) to check the health of the internal Crucial SSD. Post the compete DriveDx text report here using the "Additional Text" icon which looks like a piece of paper.
While DriveDx can run on older versions of macOS, those older versions won't be able to access the website, so you either need to be running Catalina, or you will need to download the app using another computer & transfer it to your external boot drive or transfer it using a USB stick or network transfer.