Wizard A gets 3 weapon attacks
Tenser's Transformation says:
You can attack twice, instead of once, when you take the Attack action on your turn.
So, when the wizard uses their normal action to Attack, they get to take 2 attacks (per Tenser's Transformation).
When they use the special action from Haste to take the Attack action again, however, they only get one weapon attack because Haste specifically limits the number of attacks to 1.
[The hasted creature] gains an additional action on each of its turns. That action can be used [...] to take the Attack (one weapon attack only) [...] action.
This is a specific restriction which overrides the number of attacks granted by Tenser's Transformation just as it supersedes the same exact ability as granted by Extra Attack.
Thus, a hasted, tenser-transformed wizard gets three weapon attacks.
Readying hasted Actions does not make haste overpowered
From your clarification in the comments, I will look at if doing so would make haste "very imbalanced and over powered".
In general
Rules-as-written, you can use your normal Action to Ready any available Action, while using one of the limited hasted Actions on your turn. With the proposed change, you could Dodge, Cast a Spell, or make a full set of Extra Attacks and still Ready a single attack.
Additionally, you could Ready two different Actions with two different triggers - one with your hasted Action and the other with your normal Action. When a trigger happens, you are explicitly allowed to ignore the trigger. "I Ready cure wounds to cast on the guy at my feet if he surrenders. I then use my hasted Action to Ready to attack the same guy if he instead fights back." You could only use your Reaction to respond to one of the triggers, but you could choose which one.
Dash and Disengage
Dash is useless to Ready. With your normal Action, you can Ready to move up to your speed, which is not the same as taking the Dash action. To make use of this, you would need some beneficial way to move outside of your turn without using your Reaction. Such an ability does not currently exist.
Similarly, Disengage is useless to Ready. It doesn't let you actually move; rather, it prevents opportunity attacks for the current turn.
Hide
If you find yourself in a bright room with a friendly Warlock, you could Ready a Hide action for when they cast darkness. Caveat: you can't move after this, so enemies will know exactly where you are, negating the benefits of Hide.
A Wood Elf could use Mask of the Wild to hide behind certain light obscurement that will appear later in the round (the web spell would probably apply). They would then gain the benefit from being unseen. Otherwise, just Hide on your normal turn.
Use an Object
The general statement applies here; you could now pair a readied Use an Object with any other normal Action (like a full set of Extra Attacks). You could Ready to use a Healer's Kit with the Healer feat to heal yourself or an ally. Note that magic items would not apply here, as they are not activated with Use an Object.
Attack
A Rogue can already use Sneak Attack twice per round by using their hasted Action to attack normally and readying their normal Action for outside of their turn. A hasted Rogue / Ranger with Extra Attack would gain one non-sneak attack with the proposed changes.
Conclusion
If, when presented with several options, one is (almost) always selected, then that option is probably overpowered. Would the proposed changes make haste a must-pick? Sorcerers with Twinned Spell will take it, but they do that anyway. Control-focused casters may choose it slightly more often, but fear and hypnotic pattern are encounter-ending spells that still surpass haste in most situations. Paladins and Rangers who receive haste as an extra spell will continue using it in the same situations.
A Rogue X / Horizon Walker Ranger 9 with haste would receive one additional non-sneak attack after the first round of combat. This is a significant power boost, but it shouldn't break the game. After all, a Gloomstalker Ranger 5 could be making 3 attacks in the first round of combat without spells, multiclassing, or feats! The rest of the Ready use cases are more about flexibility or niche situations than raw power.
Allowing a character to Ready a hasted Action will make the spell more powerful, as will any increase in flexibility. When presented with a modified haste as an option, it still will not be chosen every time; therefore, the changes presented will not make haste overpowered.
Best Answer
No, you can't cast a spell with your extra action from haste.
Despite including an attack as part of the cantrip, all cantrips use the Cast a Spell action, like any other spell. Haste's options are limited as you indicated, and Cast a Spell is not among the available options.
But... Divine Smite!
The paladin's Divine Smite feature is not a spell, despite being fueled by spell slots. Paladins have other kinds of smiting that are spells, but Divine Smite is not. It triggers when you hit a creature with a melee weapon attack, but does not take any sort of action; any melee weapon attack that hits will suffice.