He's not necessarily suggesting there's anything special about it being in season for 8 days.
The sentence that you quote is part of the time traveller describing day-to-day life in the world of the distant future, what the Eloi wear and how they eat. Since they're eating fruit, one would expect their diet to vary quite a bit depending on the seasons, so his remark about "in season" might be just to clarify that he ate this fruit all the time that he was there but it probably wouldn't be a year-long diet of the future.
This serves as a reminder, both to his audience and to us as readers, that his knowledge of their eating habits is restricted to a short period, and he doesn't know what fruit might be in season at other times of the year. It helps establish some realism in the story, to include the reality check that a fruit diet would be season-dependent.
But there might be something special about exotic fruit being in season at all.
As @muru pointed out in comments, for an Englishman at the turn of the 19th-20th centuries, exotic fruit would be something he'd rarely seen and maybe never seen fresh. There is no season for e.g. oranges or mangoes in Britain; they would've been imported or grown in greenhouses. As such, it would've been a source of wonder for "delightful" fruits to be in season at all, in what's presumably a distant-future version of Britain (after many millennia of climate change, tectonic shift, etc.).
I can speak to this from my own experience, growing up in Britain (even a century later than Wells's protagonist) and then visiting Mediterranean regions where orange trees are frequent - they didn't lose their wonder for me even after many times seeing them in the wild. Remember that Britain is a country where you'd be lucky to get 8 days in a row without rain.
It might indicate an earlier draft where his visit to the future lasted longer than 8 days?
This is purely speculative, but perhaps this line is left over from an earlier version of the text where Wells had his time traveller spending longer in the future, long enough that some fruits might be expected to go in and out of season. Then the comment "seemed to be in season all the time I was there" would make more sense.
I didn't go digging to find detailed info on the textual history of this novel, but I did find a paper claiming that "Despite re-reading and revising, Wells still made no changes to the chronology of the story." (That paper proposes a theory, which seems rather far-fetched to me but is supported by evidence, that the time traveller is actually a fraud who went on a bicycle ride rather than travelling in time. You might find it interesting to read - it also mentions, as supporting evidence, the same apparent contradiction that you found in your earlier question.)
