i don't know if by 'spells' here you actually meant in a shorthand way abilities like manoeuvres and such, but if not then i can't agree that the way to balance the martials with the casters is to turn the martials into casters, because then they're not really martials any more are they?
No I mean spell slots and spells prepared.
They are still martials, Rangers and Paladins all cast spells, would you say they are not martials? So do Arcane Tricksters, Eldritch Knights, several Monk subclasses and any characters with a species that gives them spells.
Plenty of martials cast spells in the game and as a matter of fact martials that don't cast spells are the exception.
While at 3rd level I do think it likely that fighters have the edge over wizards in combat, given enough encounters in the day, I think that you're going to have to back up your claim that they are "substantially better" outside of combat.
In terms of mechanics the social pillars are dominated by skill checks and Tactical Mind makes fighters by far the best at skill checks overall at 3rd level. The fact that you chose to use it after you fail and the use is not used up if it is still a fail means they are substantially better than Wizards (and even Rogues and Bards) at 3rd level.
At 3rd level Tactical Mind blows away expertise and spells that are used in the social and exploration pillars. Expertise is +2 over proficiency at this level, tactical mind in +5.5 on average and you are not locked into a handful of skills, you can use it on anything/everything and have 2 uses plus one more with every short rest.
Fighters stay among the best at the social and exploration pillars all the way through 20th level, although Rogues and full casters get competitive in tier 3 when expertise starts to catch up and spell slots get more numerous.
If you play with powergamers you see this all the time using the 2024 rules and Tactical Mind is the most common use of Second Wind at low level (after level 2). With healing potions becoming a bonus action both for the PC using it and for allies administering it to others; you hardly ever see Second Wind in combat any more between levels 2 and level 4. The only time we really see it at these levels is when you are about to do a short rest and are down a few hit points and will get the use back. It does come back into use at 5th level when tactical shift comes online, mostly on melee oriented builds that use it for the movement.