Like you I recently bought a house on a septic system that also had some storm water drainage issues, so I'm answering not as an expert, but as someone with recently-acquired insight.
How seriously to take the initial inspection..
First, since your initial inspection was performed by a different company than the one handling your yearly pumping, and since their review differs from the opinion of your regular crew ..and since you say the system is performing as it should be with no apparent issues, I'd retain some "cautiously optimistic skepticism" of the initial inspection. ESPECIALLY since those inspection notes say the drain field (absorption area) was saturated, and this corresponds with your mention of drainage issues in your front yard. It's probably obvious but, if rain events are causing ponding in your yard, then clearly your drain field will suffer compromised performance.
Lifespan of septic systems and common points of failure..
Second--a 42-year old system would concern me too, so I wonder what the potential lifespan of your actual tank is. This page suggests..
Steel tanks can last anywhere from 20-30 years, and usually deteriorate from weathering. Plastic tanks last a bit longer, with an average lifespan of 30-40 years. The longest lasting option are concrete tanks, which can last 40 years or more. ... People love concrete tanks because they last almost indefinitely, but low quality concrete that is not poured properly will fail in just a few years.
And this page says..
A concrete septic tank can last 40 years to nearly indefinitely.
So if yours was built well, and I suppose we can assume it was, then maybe your tank is hanging in there. Also since your regular pump crew thinks the system looks good from the perspective of the most easily-observed component (the tank), maybe you can feel comfortable betting on it.
..specifically, drain fields
As I understand it, when these systems fail, the drain field is the weakest link and the most likely point of failure, particularly if it was originally packed in dirt rather than gravel. (Which I think modern systems are packed in gravel?) Also FWIW, it's very possible, maybe even likely, that your drain field has been replaced at least once.
As mentioned here..
The most common and most expensive failure of private systems occurs as soil clogging and failure of the absorption system to continue to accept water.
So it may be that--if there is truly a problem--the whole system isn't in jeopardy, just the drain field beyond the distribution box.
The drainage issue..
But your mention of a drainage issue affecting your yard hosting the steptic is potentially important, especially if it's ponding over your drain field! ..in which case, I'm guessing you're considering a french drain to help move the water. It's my opinion that moving ponding storm water out and away from your drainage field should come first, for two reasons: 1) Standing water in your drain field means oversaturation is competing with your distribution lines' ability to leach effluent ..because the soil's potential to accept that effluent is reduced or eliminated. So fixing the drainage issue should automatically help your drain field. 2) You wouldn't want to replace your drain field with a known drainage issue, particularly a ponding/pooling issue, unless you handled them at the same time.
Personally, I think it would be easier to know you fixed the drainage issue if you tackle it first, rather than at the same time you replace your drain field, because that would give you the opportunity to evaluate if your drainage solution was working before you ventured into more costly overhaul of one of your home's mechanical systems. There is a caveat to this, though, you will want to make sure when your drain field is replaced, that they do not also destroy your french drain in the process ..for example by driving over the top of and crushing any drain lines.
How I'd approach this..
If I were in your shoes, I'd tackle the drainage issue first. It needs to be handled anyway, and it's definitely working against your current system, and it would be a lingering impediment to a new system.
Next, assuming your tank is concrete, and based on the observations of the pump crew that the tank itself appears to be in good shape, I'd get some quotes to replace just the drain field, rather than the whole system. Nobody likes to dump a ton of money on repairs for stuff, but if you're not too put off by the quote, I'd consider just having it done to avoid the anxiety and move on with your life.
Finally, the yard. Unless you're anticipating trying to sell your home in the near future, I would limit any landscaping I did to stuff that wouldn't be destroyed by the sort of equipment that would be used to drive over your yard digging up the system components.
To be ultra-specific, I certainly wouldn't lay sod over a potentially 42-year old drainfield, or even one under suspicion. I'd probably gamble on replacing my drain field and keeping my old tank unless the expense of replacing just the field vs the entire system (tank, distribution box, field lines) is similar enough that it's a no-brainer.
Since you're asking this in a DIY community..
If you're ambitious, and if your setting is rural-enough, you could consider replacing the drain field yourself. Be sure to look into the legality of this, but there are tons of videos on YouTube that go into the anatomy of septic systems, what they look like in various states of failure, and how to repair the failed components. Of course your old lines would need to be dug up and disposed of. You'd need a lot of gravel for below and around the lines, and you'd want to start immediately after having the tank pumped.