Hello Peter,
I am not familiar with the Truma solar system so I can't offer an specific insight it your problem, but there are some more general points that might apply to the Truma and other makes of systems.
The first point relates to the accuracy of the Voltage readings you have given. Sadly equipment gauges fitted to caravans are often far from accurate, and I have seen some gauges that are widely out compared to my calibrated measurement equipment. Especially analogue gauges were often over 1V out and current gauges were virtually useless.
Even more digital gauges cant be entirely trusted, some of the cheapest designs don't even quote an accuracy, and those that do can be as wide as +/-5% +/-5 least significant digits I do not know the quoted accuracy of the Truma Unit, nor do they quote it on their web site.
What this means is when you tell us the battery voltage might show as 15V it may not actually be that much, or it cold be more. Only a calibrated instrument can accurately tell you.
Is it actually that important? Well The chemicals and materials in batteries are quite specific, and that means they do need reasonably tightly controlled charging conditions if the life and performance is to be maintained.
I have found this web page about batteries which seems to offer quite a lot of information in a reactively easy form to take in. It is American, and I'm not claiming its 100% accurate, but in my opinion it is usefully informative:-
https://batteryuniversity.com/learn/article/charging_the_lead_acid_battery
If the maximum battery charge voltage is 15V (When measured accurately) then it does seem too much compared to the web pages suggestion of a peak voltage charge of (2.45V x 6 cells) 14.7V. But that could be well within the degree of measurement error of the Truma system.
I suggest you use a Digital Multimeter (DMM) to check the voltages at the battery. Most DMM's will be better than +/-1% accurate, and that should give you greater confidence in the readings.
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