Hmm, depends on what you'd want the output to be I think.  If you're looking for a text output in 'Total Parts Needed' that just says something like:

1 x Bottom
1 x Top with Slots
7 x Sides
1 x Top Solid Ring

And if you're producing two, you want it to be:

2 x Bottom
2 x Top with Slots
14 x Sides
2 x Top Solid Ring

Then you could try doing that with either a script or with a formula.  A script would be less work I think, and as you're comfortable with ChatGPT it should be fairly straightforward to do.  You'd make an automation trigger when a 'Production plan' record is fully filled out, and its action would be to multiply the 'Qty Needed' value against the 'Qty Per Product' value', format it as text, then update that notes field

I think it's technically possible with a formula but would take a really long time to set up and would be more fragile than the script option

I'll try the script. I just thought this would be a relatively easy thing to do. Maybe this isn't the best app for the job? 

Hmm...you could try using a new table for this instead of a script?  In that table, each record would represent a single part tied to a single production plan record.  That way you could pull the production plan quantity over and multiply it by the amount required of that part

This table would also allow you to track part usage in a structured way, and you'd have an automation to help you populate it without you needing to do it manually