Louise, this is one of the most important questions on the site, and gemma and Dhruv have already done half my job. Let me answer it directly and then give you the checks.
"About 35% per transfer" means: of embryo transfers performed in patients like the group being described, roughly 35% ended in the outcome being counted. Before you compare it with anything, ask three questions of every number. First, per cycle started or per embryo transfer? Per transfer is always higher, because it excludes cancelled cycles and cycles with no embryo to transfer, exactly the near-miss you described. Second, pregnancy or live birth? Live birth is lower and is the number that matters. Third, whose results: a whole-clinic average, your age band, or an estimate personalised to your own history? A headline figure on a clinic's website is usually the most flattering combination of those three, which is why marketing numbers compare so poorly; the standardised figures that regulators publish are counted the same way for everyone and are far more comparable.
On age, honestly: per-cycle success is highest under about 35 and declines with age, more steeply from the late thirties, because egg quality declines, so yes, the estimate at 39 or 40 will be somewhat lower than today's. That is a reason to want personalised numbers now, not a sentence. And Dhruv's point deserves underlining: because each cycle has a limited chance, the cumulative estimate over the transfers you're actually planning is often the more realistic planning number, and many people who succeed do so after more than one attempt. The site's guide to how success rates are counted covers all of this in one place.
The number that should carry the most weight for you isn't on any website: it's the estimate your own clinic builds from your age AND your two cycles, which contain real information about how you respond. That's a follow-up question, and they will expect it. And one thing a probability can never tell you: which side of it you're on. 35% happens to real people every single day.