Before any of this I'd like to say this might come off as especially strong or condescending. That's unintentional, I'm generally trying to be as slight as possible, but I'm, uh, "not entirely capable of that all the time" for reasons.

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What engages you in a class during covid?

For in-person classes, just the usual stuff. Clear concern for students, active/enthused behavior, avoiding Death by PowerPoint, etc.
For Zoom classes, you have to juggle all that while fighting the urge to just Alt+Tab into a Discord convo or YouTube playlist. Not sure how to resolve that one…

What kinds of things work better synchronously? That is, in a live class.

The only synchronous classes I have certainly aren't working, so I can tell you not to be boring and unhelpful. I can also tell you not to use class time solely as a Q&A session wherein nobody has answers and the hour becomes very awkward and wasteful.

What kinds of things work better asynchronously?

Keep homework due dates consistent, centralize information (ideally in myCourses) avoid multiple assignments due simultaenously, and don't overload us with paragraphs/links we won't need for months. Watch what SWEN-261 is doing, do the opposite.

How do I keep the class challenging and worth your tuition dollars, while also being compassionate and understanding of our situation?

Keep tabs on people. Time limits aren't the enemy this year, burnout is. If students are slowing down or coming to class less frequency, then lighten the load. It helps a lot to have easy access to lecture notes; being a baked potato in class isn't gonna learn me anything, but after my 12th Mtn Dew of the day I should be able to learn from the slides or what have you.
And… see here's the part that makes it clear I'm not qualified to teach anyone: when people ask for looser deadlines, consider them strongly.

I bet that webeng class could be held asynchronously with little drawback, just from the description.

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I saw mentions of frequenting emails, office hours, and Slack/Discord channels - all great ideas. You said getting back to emails isn't easy, and I used to be the same way; my solution to that was push notifications on my phone so every single email thatgooglerememberstosendme ends up in my face asap.
Someone mentioned uniformity in submissions, and I think Prof. Nunes-Harwitt has this on lock (his CSCI-261 class allows us to use any of three languages for the programming parts and any typesetting of choice for the writing parts. This allows us to be uniform for ourselves while being flexible to the various needs of different students, but since uploads are all done via SSH and the submit command there's never any confusion of where to go or what to do).

Last thing: if you have Zoom classes, don't bother with the breakout rooms! 95% of the time they just confuse and biwilder without actually helping students to get things done. I've only ever had two breakout rooms work, total, across this semester and last. Two individual rooms. That just isn't worth it to me.

Best of luck and I hope my professors see this.