You're right that the talk from EU about EU sovereignty is about increasing EU involvement, while decreasing US involvement. I don't agree that it's a misleading term: both "EU sovereignty" (EU independence from the US) and "EU member state sovereignty" (member state independence from the EU) are both valid uses of the term "sovereignty".

EDIT because I wanted to add some more thoughts: "Sovereignty" means "supreme power or authority". It is valid to say "EU member states should have the ultimate supreme authority and not be subservient to the EU". It is also valid to say "the EU (as in all the EU member states) should have the ultimate supreme authority and not be subservient to the US". The two ideas are not even in conflict with each other. If you think EU member states should be completely sovereign, you can still find it valuable to have EU-wide sovereignty initiatives which decrease the US's authority over EU member states.

There are two ways "EU sovereignty" can be read. One is "the EU and its member states should have the supreme authority over themselves and not be controlled by the US". The other is "the political body known as 'the EU' should have the supreme authority over its member states". I don't think these sovereignty initiatives are meant to be read as the latter.

The EU is sovereign, it is, and always has been a project for member states to tackle issues at scale that would not make sense to duplicate on a national scale, and to reap the benefits together. Don't buy into the nonsense that being stronger together is somehow detrimental to sovereignty of member states. It in fact makes them less vulnerable to bad actors on an international such as the U.S., Russia, and China.

It means some countries had already advanced hardened satcom capacities (like France which had it for a long time, lookup Syracuse satellites, it exists since 1984) in geostationary orbit, mostly for military use. It organizes the sharing of these capacities between countries immediately, before the arrival of the IRIS² constellation in low earth orbit/medium earth orbit.

The goal is to level the playing field to prevent countries to look for non European alternatives for now, which often happen in Europe when nobodies coordinates the actions of different countries when something becomes suddenly urgent (I do not thinkg it's really, but government must always show they do something, and US companies operating constellations have good salesmen).

I don't see why term sovereignty should be applied only to member states and not the EU as a whole.

It is a very vague multifaceted concept.

"EU sovereignty" in this context means being the EU being able to act with comparable agency to the US or China, as a world power. Italy or Belgium is never going to be a world power again.

Right now the EU would find it severely challenging if the US, say, broke out in a civil war and lost most of its remaining industrial, service, communications, infrastructural & military power projection functionality.

It's just a central marketplace so the governments can buy the unused capacity from these satellites with reduced negotiations with each states operating the satellites.

Most member countries are too small to have their own capabilities. It's either some sort of EU capability or outsourcing to US/China. Denmark can't afford operating a fleet of stealth bombers or whatever. In the past, basically all the big-country stuff was outsourced to the US. With Trump being elected twice this strategy seems to be a lot less safe than what everyone (except the French) used to think.