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Due to the chip shortage I was unable to buy Psoc5LP parts and was forced to substitute for an obsolete Psoc5 part: CY8C5365AXI-043. I can't find this part in the psoc creator device selector because its obsolete. Is there a way I can add this obsolete part to the list? Can I select a different equivalent device and program as if it were that one?
The answer to your first question is no. The answer to your second question is no.
You'll need to install PSoC Creator 2.2 to build your project. Even though multiple releases of PSoC Creator can be installed on the same computer, I do not recommend it. The component libraries get all messed up (first hand knowledge). So, find another computer to install PSoC Creator 2.2. And no, you cannot import a project that was created in a newer release of Creator into Creator 2.2. There is no backwards compatibility. Here's the link to download earlier PSoC Creator releases. PSoC Creator Release Notes Archive (cypress.com)
PSoC Programmer 3.28 (and maybe newer releases) supports CY8C5365AXI-043. Select Device FamilyCY8C55xx, and then select Device CY8C5365AXI-043.
Sorry for the bad news. I went through a similar cycle and this is how I solved it. Good luck with your project.