How often was C used to program firmware for 8-bit processors in the early 80s?
It would have been a rather unusual choice in 1983. True, C was slowly creeping in, but only on 'big' machines and 16 bit.
If a high level language was used at all, then it was more likely some PL/1 derivation or maybe a BASIC compiler. Especially the later was rather common on more complex 6800 projects.
[...] Handbook (1989) contains [...] C.
Well, that is 1989, 6 years later than the device (*1), when C had gained a noticeable foothold.
Keep in mind, these were the 80s, when every year delivers more changes to computing, especially at the lower end, than nowadays a whole decade brings.
A Short Look at the Transition to C in Time
To put this into perspective (*2), the first Microsoft C compiler, which was not even K&R compliant, came 1983 and wasn't their own development, but a relabeled Lattice-C. It wasn't until 1985 that MS finished one of their own (MS-C 3.0).
For common 8 it systems, BDS C for 8080, of 1979, might have been the first, followed by Small-C in 1980. Both kinda limited systems, more like proof of concept. The first major commercial product I can think of would be Aztec-C in 1982. Eventually the 8 bit compiler for desktop systems (*3) - and that was what C was targeted at in the beginning. As alternative to build in BASICs and PASCAL - which was the coming language of the 1980s. Just think Turbo-Pascal.
Which is a good keyword here, as Borland was, at least during the 80s, quite good in delivering what the marked wanted. Still, their Turbo-C only came in 1987.
Another good marker might be Apple and their Mac series. All Lisa and later all classic Mac system software and most applications were written in Pascal. Yes, this includes explicit the OS. It wasn't until 1987 that Apple even included a C interface (and compiler) to MPW. Pascal Support was, way into the PowerPC age the way to go.
The second half of the 80s is when C became a somewhat relevant language in microprocessor programming, one that made sense to support (like in that data book). And it wasn't until the very late 1990/early 2000s that C - or better C++, became the first stop for many areas.
Now, for your actual project way more information would be needed to decide - starting with CPU, System and Size but as well why you assume it's HLL in general and C in particular.
More likely I'd say the assembler used was macro equipped and a library (*4) of structure and data macros was used. The resulting code may quite like coming from an HLL - after all a compiler doesn't do much different by modifying and stitching code sniplets.
*1 - The product also had some development time, so language decision must have been way before 1983.
*2 - This is about C becoming a the one language across platforms, supported by essentially every CPU, OS and development tool, one that had to be supported, in ubiquitous use from embedded 8 bit to supercomputing. It is not about usage at all, as there have always been forerunners, individual users and projects using non mainstream product - which C was clearly before becoming so prevalent that people assume, without further research the language to be used to generate code.
*3 - Which BTW is opened up by now and well archived.
*4 - Guess what we called 'A Library' would be today called a framework and a documentation loaded with more 3 letter words than assembly instructions used.