This shield is very powerful
By the first benefit alone, the shield is comparable a Shield +2. Having half-cover grants +2 AC and DEX saving throws. The reason this is not strictly better than a +2 Shield is because it does not stack with other sources of cover (and can be nullified by features that ignore cover). A +2 Shield is a rare magic item which according to DMG guidelines is appropriate for characters of level 5 or higher.
The second benefit as you note is extremely good. Spending half of your movement is a negligible cost in a lot of situations, especially on a paladin. With access to Find Steed or other mounts, you aren't using your own movement for anything else so spending half your movement to get 3/4 cover is almost free. Even if you don't have a mount, you may not need to move over half your movement often enough that you get the chance to activate this. Having +5 AC for a round is comparable to the Shield spell. Yes, this is just a lvl 1 spell but it requires a reaction to use and usually expends some sort of resource (a spell slot or charges on a magic item)
The third option alone is actually not that strong. Expending your action to grant an ally half-cover is a fairly weak option when standing in front of your ally usually already does this. Having an extra option for an action doesn't really hurt though and in a situation where you can't reach your opponents and have nothing else to do it might be useful.
All of these features together make the shield an incredibly powerful option, especially considering that you can purchase these for 75 gp. I suspect anyone with 15 STR that can use a shield would probably use one.
Is this actually a problem?
Whether having this item in the game is actually an issue is doing to be very group dependent.
For example, if all the PCs have access to very powerful items it might just be fine. The DM may just be planning to throw more powerful encounters at your party or just wants to run a game where the PCs can win encounters fairly easily.
Having a very high AC also does not mean you are invincible, see this related question.
The DM may simply not have realized how powerful this shield is
This can happen often. The DM hands out an item without realizing just how powerful it is until it actually comes into play later.
The important thing to do is to assume good faith on the DM's part. Don't accuse the DM of handing out an OP item. Instead, try to explain how this might affect the game in ways that may not be fun for the group. Let me give you an example:
In a homebrew campaign I played in, after defeating some orcs of Gruumsh, the DM allowed us to keep their blood and apply it to any weapon for a permanent +1d8 damage (like the orcs' trait). While it seemed fine at the time, an extra 4.5 damage per hit for the martial classes was enough to feel unfair on the wizard and bard, who were now resorting to using weapon attacks instead of cantrips. So, after discussing this with the DM it was reduced to 2 extra damage and limited to mundane weapons. I honestly still felt it was a bit much at the time (I tend to be a bit of a balance maniac) but I let it go and it turned to be fine during gameplay.
My takeaway from this is to let it play out a session or two and see what happens. If it is causing actual issues and causing the game to not be fun it should be fairly noticeable and you can then approach the group to discuss how to go about improving the situation.
Maybe it is agreed that the item should be nerfed. Maybe the DM just hands out similarly powerful magic items to the other PCs and cranks up the difficulty of the opponents. Or maybe something else entirely.