Try using the Game Bar overlay, it came out prior to 1903 update (press windows icon + G, or press the Xbox logo button on a controller). From there you should be able to see a list of your friends online, right-click on their name and invite them.
Accepting invites now is a bit more convoluted than it used to be, but you should find a list in the notifications menu on Game Bar in case you miss the pop-up.
The new app needs a bit of work alright. We used to use the old Xbox App for party chat because a couple of the crew were on Xbox One and we got used it being handy to just invite party to game. Now that's not really user-friendly and all of us are now on PC, we just use Discord for VC and join on one person rather than send invites.
Regarding updating Windows. 1903 is still rolling out. If you want to update yourself before it appears in your updates, go to the Windows 10 Update Assistant page on the Microsoft website. Bear in mind that the update will take about an hour, maybe longer, and if you have an AMD processor it might be a good idea to update the drivers for it first (though I didn't, I've a 1700x and not had any issue in the week since I updated a week ago). 1903 also doesn't like Battleye at all, so if you also play PUBG, Ark or other games that use it, you might want to hold out.