I think having a View with the archived projects would be better. Anyway, Airtable does not have a native feature to do that (it has no sense to me), but you could do it with Zapier: https://zapier.com/zapbook/airtable/

I’m with @Elias_Gomez_Sainz in that I see little benefit to archiving projects, as they are unlikely to reach a quantity approaching an Airtable base or table limit. That said, if there are other reasons — be they operational or aesthetic — for doing so, I’d suggest taking a look at the method I outlined in this post. Such a technique relies upon standard Airtable functionality to create and populate the archived record, looking to middleware (Zapier, Integromat, IFTTT, et al.) simply to trigger the process. This protects against possible synchronization, data loss, and recovery issues in the case of a failure in the Airtable<->middleware work flow.

Keep in mind this process does require an additional copy/paste action be taken in the destination table, which could either also be handled by middleware on a record-by-record basis (it, too, is a two-step action, so supportable under a free Zapier account) or manually for an entire table’s worth of records (e.g., click column header to select entire column, press Ctrl-C to copy all values, click header to select destination column, press Ctrl-V to paste all values).

The procedure described only works to replicate columns from one table to another within a single base. To replicate across bases can only be done through middleware using a multi-step action. However, the packing and unpacking of a ‘portmanteau’ field can still be used, if desired.