The mention of Act Together here is not to say you get everything under the 'Eidolon' entry with the dedication feat except for it. It is there to underline a consequence of not having Act Together.

So, the dedication feat says exactly what it provides : an eidolon and the Manifest Eidolon activity.
It also says what you can never gain or use : any Tandem action.
And it reminds readers that this means no Act Together and thus no separate Exploration activities.

The obvious problem with this is that the section in the physical book for Eidolons has a LOT of stuff in it. And if you say that you only get what's explicitly listed and you don't get Share Senses becuase the dedication doesn't list it... then what about the rest of it?

By this reading, you also don't get "Gear and your Eidolon" or "Lost and Altered Actions", because they're also distinct things and the Dedication doesn't mention them.

It doesn't fly. The whole section in the book is written as one long thing, not a bunch of distinct things. The Eidolon section itself has:
1 A long block of text
2 A sentence leading in an action
3 An action (Manifest)
4 A sentence leading in an action
5 An action (Act Together)
6 A sentence leading in an action
7 An action (Share Senses)
8 Another block of text about hit points
9 A subsection about gear
10 A subsection about lost/altered actions

It makes sense to say you get 1-10 except 4 & 5, because the dedication says you don't get 5. It DOESN'T make sense to say you get 1, 2, 3 (because the dedication says you get it), 8, 9, 10, while claiming you don't get 4 & 5 because the Dedication says you don't, and you don't get 6 & 7 because the Dedication doesn't mention it.

The Dedication also doesn't mention 8-10. So this means Dedication Eidolons don't get rules on how lost actions work and get either no restrictions on gear or no access to gear whatsoever. If Share Senses isn't part of the "Eidolon" entry the Dedication says you get, than neither are any of these things, since they come after Share Senses.

Saying they do get those things, despite them not being part of the "Eidolon" entry (which is the entire argument for why they don't get Share Senses) doesn't fly when Share Senses is earlier in the same section. It's cherry picking something in the middle of a section and going "this isn't part of the section and doesn't count despite stuff after it still counting because reasons."

That's not how the physical book is laid out, and that's not how English works. The whole Eidolon block is one set of rules. The fact that they neglected to mention something doesn't mean it vanishes from that block of text, especially when you're not applying that standard to the entire block of text.