I actually read it as it was posted (very clearly):
"I'm trying to get to Gold. My account shows under "How to Upgrade my tier" that I have until 01/07/2025 to meet the requirement."
I think you understood it correctly the first time (there's no "card expiring" or anything", this just concerns the upgrade to gold, not a renewal of silver), however I'm afraid the feedback you gave in that post was also not correct.
Here's why: This is what a silver account looks like:

The expiration date on the actual card is 22/03/2026.
So far so good, you were both correct in that comparing the card's expiration date with the deadline for meeting *that same card's* criteria, you get a difference of 1 calendar day.

However, like I said, this is not the subject here. The subject is upgrading from silver to gold. Which is a rolling date (year) depending on the date of the oldest flight, which counts towards upgrading, + 365 days.
Here's where I think Aegean's IT has messed it up badly for people playing the system on its very edge:
As you can see, the "how to upgrade my tier" part also has a date (deadline) under it. This is displayed next to the "to maintain my tier, I need:" in almost the exact same way, but with the not so obvious difference, that the former reads "until" (date) while the latter "up to" (date).

The logical conclusion is, that whatever is valid for the latter deadline is also valid for the former deadline.
The problem is, in the aforementioned example the first flight that counts towards reaching gold was taken on 15/07/2024!
This means, that the 15/07/2025 will be the 366th day, which means, that by then, the tier miles from the flight taken on 15/07/2024 will have expired and will get added to the amount required to upgrade to gold.

The greek text on that page reads "μέχρι και" for retaining silver and just "μέχρι" for upgrading to gold. The "και" in this case is (how I assume Aegean means it) the logical AND (so it's more like "up to AND including" whatever date is shown next to it), whereas the "until" part means "not including" whatever date is stated.

Of course this is a very bad way to communicate a deadline, the language leaves room for interpretation, the fact that the almost identical information right next it regarding renewals includes an extra day is very misleading, but, again, this is not based on my interpretation of this information, but on the fact that tier miles expire after the 365th day, and the 365th day in the OP's case is June 30th, as I am pretty sure (that's something harry0233 could confirm) he has credited tier miles on July 1st 2024.