I finally figured this out. Posting a reply in case anyone else finds this post and has this problem.
Open Health app, open Steps section, scroll to the bottom to Data Sources & Access, click Edit in the top right corner, and then scroll down to Data Sources and drag Health to the top of the list. (In most cases you’ll want your watch to be second and your phone to be third).
The order of these sources determine which one is seen as more accurate or preferred when there is overlapping data in the same time frame (which Apple doesn’t disclose how they measure time frames since adding steps via Health app doesn’t allow you to enter a stop and start time). When your device that’s acting like a pedometer, such as your watch, says you weren’t walking but you entered steps that you earned from something like an under-desk elliptical, Health will ignore the manually added steps as being an error and ignore the steps you added by hand. When you move Health to the top your manually added steps will be seen as legitimate over other devices. This means you may lose some steps that your Apple device registered with its pedometer function in the same time frame (theoretically anyway… I haven’t seen this happen in my data for the past 40 days) but this will be a much smaller loss (probably under 100 steps) compared to the hundreds of thousands of steps you’re trying to add manually. I find this to be an acceptable risk and much easier to live with than having to log my manual steps into an additional app.