My daughter has the same issue. She would say she didn’t have homework even when she did, or she’d say she turned it in when she didn’t.
Something that worked for a while with her was that once she had a missed assignment in a class, she had to start having that teacher sign a sheet (which I provided) on Fridays that indicated whether or not she still had missing work. If she had missing work on a Friday or she didn’t get a signature, she didn’t get to go anywhere that weekend and we gave her plenty of electronics-free time to get it done (even if she finished the assignment Friday night, she still couldn’t go anywhere the rest of the weekend). We only did this the last couple months of school last year, but it definitely made a difference and we plan on using that this year as well. We will probably start fresh each semester or quarter (not requiring signatures unless/until she misses an assignment)
Our daughter’s school is also very chromebook oriented, so teachers enter assignments & tests online. So for a while after she misses an assignment, we’ll sit with her each night to go through each class’s web page. After a couple weeks of checking nightly with her, we’ll pull back and let her check assignments on her own, but if she misses one, we start checking with her every night again (which she doesn’t like). She will continue to check on her own for at least several weeks after we are done checking with her, so I know it’s working – just need to aim for longer time frames. I’m really looking forward to seeing what other solutions people have come up with too.