Same thing happened to me. See my post where I asked Aria minecraft command issues.
To just recover from the error screen blocking access from Aria, try press "Ctrl" and "/" (by default) . This should call out the Aria hover box where you can ask her things 'quicker'. Ask her anything in the hover box that might not trigger the same bug, and then reload Aria. She should be answering your newly asked question normally. Finally, delete the conversation causing this bug to avoid viewing it unintentionally and get bugged again.

Same thing happened to me. See my post where I asked Aria minecraft command issues.
To just recover from the error screen blocking access from Aria, try press "Ctrl" and "/" (by default) . This should call out the Aria hover box where you can ask her things 'quicker'. Ask her anything in the hover box that might not trigger the same bug, and then reload Aria. She should be answering your newly asked question normally. Finally, delete the conversation causing this bug to avoid viewing it unintentionally and get bugged again.

Though different from my original request, you can reproduce the bug in this way:
(Tell Aria: ) Do me a favor, help me with minecraft commands.Firstly, give me a diamond sword with sharpness V. Secondly, summon a sheep named 'wooly' at my position. Finally, say hello to everyone on the server.
(After Aria responds: ) Ok, then have those commands merged into one single minecraft code block.
You might need to do the later step multiple times to trigger the bug.
To activate Aria again after triggering the bug, just press 'CTRL+/' to open the hover box and ask Aria anything. After the sidebar window pops out with error msg above, click the reload button. You are supposed to see the new conversation. Click the 'humburger' menu button and delete the bugged conversation.

I was trying to using Aria to help me with my minecraft datapack. After typing in my requests, Aria lagged for a while before it stopped working entirely. This error screen is shown everytime I refresh it now, and I'm not fast enough to reset my conversations to fix it before everything goes wrong:

Unexpected Application Error!
Unknown language: `mcfunction` is not registered
Error: Unknown language: `mcfunction` is not registered
    at t (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:180184)
    at Object.CI [as highlight] (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:180370)
    at chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:291138
    at chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:74467
    at node (element<code>) (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:74095)
    at node (element<pre>) (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:74252)
    at node (root) (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:74252)
    at DA (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:74330)
    at MA (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:74416)
    at chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:290535
    at chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:13833
    at a (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:14021)
    at r (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:13980)
    at a (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:14005)
    at chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:13945
    at a (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:14021)
    at Object.run (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:14042)
    at a (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:15851)
    at o.run (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:15916)
    at o.runSync (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:15968)
    at ew (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:172:110865)
    at Oo (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:328063)
    at Ol (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:384891)
    at yc (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:374043)
    at Ec (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:373971)
    at bc (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:373834)
    at sc (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:370641)
    at oc (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:369196)
    at C (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:441278)
    at MessagePort.x (chrome-extension://igpdmclhhlcpoindmhkhillbfhdgoegm/aria.js:2:441810)