I see what you mean about the engraving, the first ST looks bigger than the rest, but the engraving on the bracelets can be a little wayward so its not a red flag unless there is anything else amiss IMO.
Modern Omegas do usually have the metal stated on the back or lugs but I am not sure that is the case where mixed metals are used like here. This also isn't a red flag to me.
Does the serial on the watch match the cards? If not walk away.
Here is the omega page for that watch, the front and back look similar at least:
https://www.omegawatches.com/en-gb/watch-omega-constellation-quartz-27-mm-12325276055004
Be aware that while the date on the cards suggests it was sold last month, the style of the cards and the instructions version number printed on them (Operating Intructions 12) suggest it may have been made quite a few years ago, they are up to at least version 20 at present. Also note it is showing as discontinued on the link above, so while sold new recently, it might have been made at a guess around 2015 or so. The 52000 country code on the cards is correct for a Hong Kong market watch by the way.
I wouldn't necessarily assume the manufacturer warranty applies unless you can check it with an OB. The date of sale might have been added later by an unscrupulous reseller, but if it really was sold last month then you should have most of the standard 5 years warranty remaining.