Minecraft 1.21.1 Neoforge
I'm trying to use AE2 to auto-craft some things. Steel Cutting machine may stuck under these conditions:

1. Insert ingots to create some rods
2. Some rods created and now some of them are still in the output slot (not imported yet to AE2 system)
3. Insert rods to create bolts
4. Machine goes to infinite pause in this state. For example, 6 rods are in input slots and 3 rods in output and rods from output slot are never imported.
5. If get rods from output slot manually then machine resumes.

The same issue with Steel Wiremill

1. Insert plates to create wire
2. Insert wire to create fine wire
3. Machine goes to pause with wire in both input/output slots

How are the items supposed to be taken from the machine output? Of course the machine will "lock up" if nothing is taking the produced items.

Items are taken by import bus from AE2, but it works with some delay, so produced items stay in the slot for some small time and later they are slowly removed. But if input slot get the same items as output slot, then importing stops and machine cannot continue.

Full layout is:
Import Bus (AE2) behind machine
Steam pipe below
Pattern Provider (AE2) above.
Pattern Provider contains receipts ingot->rod and rod->bolt.
If start auto-crafting some item which requires many bolts, then with some chance possible such situation, when some rods from (ingot->rod) receipt are still in output slot, but other rods from (rod->bolt) receipt are inserted in the input slot and then machine freezes.

AE is probably trying to pull from the input slot.

May be, but there are no similar issues with Mekanizm machine which also frequently uses similar scheme:
iron->enriched iron
enriched iron->steel dust

Okay it's actually a bug with the AE2 import bus.