The ten-cent version: Yes, as far as I am aware, the StG. 44 is the first 'assault rifle' to see widespread issue. However, its predecessors saw some combat in Wehrmacht service as well. The Federov seems like a competitor at first, but when you dig deeper it turns out to be a horse of a different color altogether.

Trying to figure out the 'first' of something is something of a semantic problem. There were designs that predated the Sturmgewehr, including its direct precursors the MKb 42(H) and MKb 42(W). The MKb 42(H) saw some combat service on the Soviet front as early as 1942, though I do not believe the 42(W) ever did. The StG. 44 was certainly the first of its type to see anything approaching mass-issue, When I say "its type" I mean an infantry shoulder arm - a gun designed to be fired by one man, from the shoulder, rather than a light machine gun for instance - that checks all of these boxes:

1. An intermediate cartridge. This is a cartridge in between a full-power rifle cartridge (such as .30-06, 7.92x57mm Mauser, 7.62x54r, etc) and a pistol cartridge (9x19mm Parabellum, 7.62x25 Tokarev, etc). This picture from Wikipedia shows a size comparison (the StG. 44's cartridge is on the far left).
2. Fires from a closed bolt. This means that when the gun fires, the bolt cycles all the way and locks forward, putting a new round in the chamber before the trigger resets. Closed bolt mechanisms are in contrast to open bolts, in which the trigger resets when the bolt locks back, and then the bolt goes forward to push a round into the chamber & fire it. Closed bolts are inherently more accurate, but are less effective for sustained fully-automatic fire; this is why machine guns, and some submachine guns like the PPSh or Uzi, are open bolt designs. However, the assault rifle is a rifle first and foremost, and should therefore be closed bolt for accuracy.
3. Select-fire. It should be able to fire in semi-automatic - one shot per pull of the trigger - as well as fully automatic - the gun keeps firing as long as the trigger is pressed down. Furthermore, it must be controllable in full auto. Different armies have held different criteria for 'controllable' of course. The Soviet criterion of hitting a 1.5m by 1.5m target with a burst at 100m will do as an example.
4. A detachable magazine, probably with 20, 30, or more rounds.

These criteria eliminate many of the other possible 'first assault rifles'. For instance, the FG-42, although doctrinally filling a similar spot to the StG. 44, fired the full-power 7.92x57mm Mauser round. The MKb 42(H), although it saw combat, fired from an open bolt, and in any case can't really be considered to have seen significant combat usage. Curiosities like the Italian Modelo 1921 or the prewar German Vollmer M35 never saw combat at all and are, therefore, curiosities. But what about the other one you mentioned? What about the Federov? It seems to fit the bill, at first. It even fires an intermediate-seeming 6.5mm round.

The Federov is, despite superficial similarities with assault rifles - as well as, especially confusingly, the 'avtomat' name, which it shares with the AK series - really more of a light machine gun or an automatic rifle like the BAR or the Bren. It was issued as a two-man crew served weapon. One man fired it from a bipod and the other served as an assistant gunner, feeding him spare magazines and acting as a spotter. EDIT: Thom430 has pointed out to me that, as standard, the Federov was only issued with 3 magazines, and so much of the assistant gunner's job was to reload magazines via stripper clips. This is pretty similar to how two-man Bren gun teams in British service worked.

Federov himself was influenced by the French Chauchat light machine gun. In Monetchikov's "История русского автомата" (Istoriya russkogo avtomata - The History of the Russian Automat), Federov's 1915 visit to the trenches in France is described, including this helpful excerpt from his memoirs:

“My attention was also attracted by several machine gunners with the latest Chauchat system machine guns, which had just been introduced into the French army. A light machine gun developed a rate of fire of 150-200 rounds per minute and could replace about 15 riflemen ... Only here, in the trenches near Mont-Saint-Elua, for the first time I personally became convinced of the urgency of the need for new weapons for us ... Not an automatic rifle, but a machine gun, it was first of all necessary to develop for the Russian army! Here, in the trenches, the idea arose of turning an automatic rifle into a type of weapon close to a light machine gun - something between a rifle and a light machine gun, then. What we now call an automat."

(Translation via Google translate, as my Russian is sadly still pretty rudimentary.)

Now, Federov himself initially conceived his automat as a full-power semiautomatic rifle, firing the 7.62x54r round which was already in service in the Russian military. The experience of the Russo-Japanese War indicated that the weaker, softer-recoiling 6.5mm Arisaka round had close enough wounding behavior to the 7.62x54r, and could be a good candidate for a semiauto rifle cartridge, where the lower recoil force would result in less parts breakage and better controllability. Federov himself seemed to be opposed to this idea, though, as the 6.5mm was not ideal at the longer ranges needed in a support weapon.

So, despite the what-ifs of some interwar oddities, and the red herring of the Federov Avtomat, the StG. 44 does really seem to be the first widely-used assault rife.

Sources & Recommended Reading:

Handrich, Hans-Dieter and R. Blake. Stevens. Sturmgewehr!: From Firepower to Striking Power. Cobourg, ON: Collector Grade Publications, 2004.

Monetchikov, Sergey Borisovich. История русского автомата (Istoriya russkogo avtomata - The History of the Russian Automat). Saint Petersburg, Russia: Atlant 44 Publishing House, 2005. The whole thing is available here, as well: https://coollib.com/b/195891/read. Unfortunately, it's only in Russian.

Forgotten Weapons. "How Does It Work: Open Bolt vs. Closed Bolt Firearms." YouTube video, 4:35, January 3, 2019. https://www.youtube.com/watch?v=Ga4uoWmfEt4

F., Nathaniel. "Before The Sturmgewehr: Assault Rifle Developments Prior to 1942," The Firearm Blog. April 2, 2014. https://www.thefirearmblog.com/blog/2014/04/02/sturmgewehr-assault-rifle-developments-prior-1942/

I would also like to tip my hat to /u/JustARandomCatholic and /u/thom430 over at r/warcollege for providing some of the fodder for this in various discussions; thom430 in particular was the one who tipped me off to the existence of Monetchikov's book.