Reproduction steps:

1. Load attached world (use either survival or creative mode)
2. Use command /tp 2310 -46 -3875.5
3. Shoot 3-5 arrows into the wool block directly next to the sculk shrieker (take care they don't return to inventory)
4. Flip the redstone lever on the redstone lamp (lamp should now be ON)
5. Wait for wardens to begin spawning on the glass platform
6. Verify that messages "warden crossed tripwire" and "hopper clock pulsed" appear
7. Use command /tp 4951 -49 -3780 (coordinates to a set of ancient city sculk sensors/shriekers)
8. Wait several seconds to verify that messages "warden crossed tripwire" and "hopper clock pulsed" still appear in the chat log following the tp command. This means that
   1. The chunk loader is working
   2. The sculk shrieker in Step 2 is still summoning wardens
9. Walk around the nearest sculk sensors to activate the nearby sculk shrieker

Observed Results: Shulk shrieker from Step 9 spawns a warden

Expected Results: Shulk shrieker from Step 9 should NOT spawn a warden

From the wiki: "This means that if a player triggers one shrieker, they are completely unable to trigger any other shrieker within 10 seconds." (https://minecraft.wiki/w/Sculk_Shrieker#Spawning_wardens)

A sculk shrieker near 2305, -50, -3852 in my single player world is activated every 10 seconds by arrows on a block (shot by player). With a nether portal chunk loader, it still activates and runs even when player is at coordinates 4946, -48, -3774.

I verified it was still operating using command blocks to announce when the hopper clock pulsed, and when a new warden entered the farm's water-stream (see screenshot1 and screenshot2).