ATEM Mini Pro can it program out to record & to a projector

Obviously new a this. We started to film the festivals we put on and did fine at first until we decided to enhance. Ran into a brick wall. We wanted to project what we were filming on big screen because we have multiple stages so there is no downtime. After researching it appears this just isn't possible with the equipment I have unless somebody has some ideas. The problem I ran into was that apparently I cannot record/stream and output Program to anything else like a projector. If it is impossible with the ATEM Mini Pro (I was going to step up to the ISO version, but see that it is the same issue the same issue so I may need to go bigger) to have the program go to two different outputs (record/stream & another device) can I do this with the Extreme, or something else?
Can I get creative with software? We always want to be able to see the multi-view so that we can PTZ the cameras and make cuts, but also have just program out in the scenario I'm facing. right now we just record out to an SSD drive, if I record out to my computer (which I'm assuming I can do without a capture card) and I run both black magic software, and OBS on the computer get complicated by letting OB show me the multiview so we can manage the cameras let's and then let the ATEM always be set to Program view only so I can record it on my computer and let the HDMI out show just the program and I can display that anyway I want. so it would kind of look like this I have OBS set up to multi view the cameras so we can control them, but not have control the ATEM switch.

If it is impossible with the ATEM Mini Pro (I was going to step up to the ISO version, but see that it is the same issue the same issue so I may need to go bigger) to have the program go to two different outputs (record/stream & another device) can I do this with the Extreme, or something else?

...not sure what problems you may be having but if you want a dedicated multiview you will need to step up to the Extreme (ISO or non-ISO).

The rest is relatively easy: hdmi out 1 is your program feed to the projectors, hdmi out 2 is your multiview. You can record via the usb-c output either to an ssd or to obs. Alternatively, you could also record the hdmi program output with a hyperdeck hd plus (or the hd mini using a converter) by looping through the hyperdeck to your projector(s).

Thanks, That's what I thought. I'm upgrading to the Mini Extreme ISO anyway.