These data are quite difficult to collate - as you've pointed out, results are most commonly reported at the county level, and congressional districts only perfectly overlap county borders very rarely. If states themselves don't provide congressional-district-level totals, the data must be calculated by hand, relying on individually totting up data at the individual precinct level. This is often difficult; as shown in my answer to this question, where I was unable to calculate exact results for Texas' 15th district due to inconsistent online reporting across counties.
However, this work is being done for the 2020 election, and has been done for previous recent elections by the Daily Kos elections team as part of their "Pres-by-CD" project. The results can be found here, and are being updated on a state-by-state basis. In 2016, this work was completed at the end of January '17.
For perhaps an insight into how painstaking this work can be, I recommend this article - to pull out one example:
But the states that don't offer precinct data in one central place?
Those states make life hell. For them, you have to go county by
county, and that's a brutal process. Sometimes counties post precinct
results online, and some are in usable formats, like spreadsheet
files. Some are less useful, like native electronic PDFs that can be
converted with software but require a lot of effort to reformat.
The worst, however, are in scanned PDFs that are just brutal to
convert—OCR typically chokes on them—and usually have to be reentered
manually. And some results, believe it or not, are handwritten. The
most amazing of all was an Excel file where numbers were represented
by clip art images. (And yes, we actually once needed to use that