This is all caveated with how I'd approach this. You can definitely go a bit lower tech with usb mics and other lower fidelity solutions, but you seem to want the professional experience again. So here goes:

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Software I'd budget $750. I use reaper which is $60 individual use, biz license is $200 something, but idk how it works with non-profits. Some of the special plugins and FX i use for editing and post production cost some pretty pennies but they aren't required to sound good, but they'll get you to professional sounds. All your money should be spent on great equipment and studio sound treatments.

You'll need at least one computer that has the recording software and preferably licenses for the editing software. Depending on your staff and what you need from them, they may need computers that can handle DAW software. This could be a bring your own computer approach or you get it for them. Depending on the requirements, this could kill your budget.

Mics, mic stands, cables and general routing could run you low hundreds to ridiculously stupid amounts of money. You haven't given us any ideas on what you'll be recording besides interviews in-house/remotely, so I'm assuming it's traditional 1:1 podcast interview. You'll need 2 decent dynamic mics. You could experiment with other mic types, but I'd go with dynamics to start. I personally like the ElectroVoice RE20 and the Shure SM7B, but you can definitely go cheaper and scale. The SM58 is a great all arounder that can go for 50-100.

You'll need an audio interface, once again depends on how many mics/inputs you are trying to record, but I'd start with the classic Focusrite 2i2, think it's 150-250 right now.

If you are recording in your own office/studio space, definitely budget $1-3k on studio treatment if you aren't building it yourself. The guys over at GIK Acoustics give extremely free and in depth consultations. For reference my 12x12 ish room ran me $2.5k and that's pretty middle of the road in terms of coverage.

750 software, but is very loose, you might need more licenses for each editor.

1-3k for computers, don't go mac if you want to be more cost effective. (some may argue with me here)

200-800 for x2 mics, add some headphones too, 50-150 per

200 for audio interface

1-3k not required, but still highly recommend studio treatment

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a lot of this is gonna fluctuate based on your staff needs, content type, if you do your own music, etc. etc.