Update just received from the DEVONthink forum:
At this time, only PDFs have in-document search capabilities.
Support for other formats is on our list of future enhancements, but it wasn’t feasible until we released our new text editor in DEVONthink To Go.
The new text editor has been out for a while (May 2022). Like most things with DTTG things happen slowly.
I wish there was another mobile first app that had the linking per file, as I find that very useful across Mac and iOS. But using DTTG for notes has definitely felt like square peg in a round hole type of affair.
Will be interested to hear if this gets you back on the obsidian indexed train or you will stay with Apple notes! 
No, I don’t see myself going back to Obsidian. While I like some of its features, I find a lot of friction in using it, especially when I desire to attach PDFs and add tables. I have made a firm commitment to myself that I am sticking with Apple Notes for personal professional note taking, unless and until syncing crashes again in a significant way. If so, I will feel compelled to move all of my note taking to DEVONthink or some other app. I am hoping against hope that Apple Notes syncing will continue to work…
I’m doing all my notes in DT (except for quick notes that I will delete and shared lists go to Apple notes). If devonthink to go added templates for text documents (currently only able to use this for pdf), and ability to have a quick toolbar like obsidian with current date, etc would go so far in narrowing the gap. Also I wish DTTG had a search that was touch friendly, it’s ridiculous to have to manually type the search operators on mobile (I tolerate it on mac since I can turn into a smart list, not an option on mobile).
All that being said, nothing is perfect, and my use case of having files/group/meeting notes etc with a link in Apple reminders or Apple calendar really makes it work well.
DEVONthink ToGo search works fine for many (if not all) document formats if you search outside an open document. This search feature very comprehensive.
Inside open PDF, there is a “search icon”.
Only in an open document is search limited to a PDF.
See “Help” in DEVONthink ToGo for the rich set of search criteria.
This is exactly what I will do if sync stops working again in Apple Notes. AN is easier, faster, nicer and better integrated, which is why I prefer to use it but I have to be able to depend on it. Then, of course, there is the “lock-in” that I do not like.
I received a good suggestion in the DT forum echoing suggestions in this one.
@Bmosbacker I was sparked to look for myself on this as I never noticed the missing find inside a document. I must be using PDF’s when I needed a find in an open document, or maybe I never found the need.
But I notice that when doing a search from outside an open document (pulling down the search box), the search text is quickly found. DEVONthink ToGo will find text in PDFs, Rich Text, Text, Markdown … (didn’t try to notice any more). And in Help on DEVONthink ToGo there is documentation of the extensive search criteria available.
So while we wait for searching inside an open document (for files other than PDF), there is quite a lot of searching capability already there that can be exploited. Give it a try.
I just tried the suggestion. It enables me to find the document with the specific phrase I’m looking for. If I then open the document OUTSIDE of DTTG I can search within the document. This is a workaround without too much friction. This will work and I avoid even the temptation to change apps. 
It does not search inside a text document unless you use the content: first modifier however. This seems to be a known issue per the DT forums.
Yes I can search the document but you have to specify content to search more than titles. If this is not how it works for you I will report the bug.
Sorry, but none of the above is as I experience or shown by my testing just today, albeit limited.
I suggest you post these observations on DEVONthink’s DEVONthink ToGo forum and lobby for the “bug” you see to be fixed.
