Yes, you can install macOS on an external SSD and it will likely speed things up.
➡️ Download the macOS upgrade installer app:
Click > macOS 14 Sonoma.
Once downloaded, double-click the “Install macOS…” app now found in the Applications folder to begin the installation process, selecting the ext drive as the destination.
Please see > How to download macOS - Apple Support.
❗️– IMPORTANT –
Let's see if we can figure out why your Mac is running so slowly.
Please run an EtreCheck evaluation of your Mac and post the generated report back here in a reply. EtreCheck is a safe and highly regarded utility from a trusted developer and respected ASC contributor. The diagnostic report will not include any personal info. It simply gathers specifics about hardware performance and installed software that might be in conflict with the OS.
Please navigate to EtreCheck.com and download the free version. Be sure to Allow Full Disk Access when you install the app. Once you’ve run the app and created your report please post it with your reply to this message.
Please note you must upload the full report. To see how, please click > How to use Add Text when posting… EtreCheck Report.
We’ll use your EtreCheck report to look for the things that may be causing your problem and advise how to correct them.