Octo is installed independently of Tentacle, so upgrading Tentacle will not have an effect. Octo can be installed either as a dotnet tool or by unzipping an archive. For the archive version there is no dependency on a specific version of the .NET core runtime but as a tool you must have .NET core SDK 2.1.x installed. (This is called out in our docs here: https://octopus.com/docs/octopus-rest-api/octo.exe-command-line/install-global-tool).
Your options would be to install the 2.1 SDK, or use the archive for your chosen OS which is available from our downloads page: https://octopus.com/downloads
Just following up on this one. We are currently working to distribute Octo as a self-contained executable, which will remove the requirement to have .NET core installed. You can follow progress here: https://github.com/OctopusDeploy/Issues/issues/6128