Short answer: No.
Extracted from the Simulacrum spell description:
Duration: Until dispelled.
Thus, an ongoing magical effect.
And also:
It appears to be the same as the original, but it has half the
creature's hit point maximum and is formed without any equipment.
Otherwise, the illusion uses all the statistics of the creature it
duplicates.
The simulacrum is friendly to you and creatures you designate. It
obeys your spoken commands, moving and acting in accordance with your
wishes and acting on your turn in combat. The simulacrum lacks the
ability to learn or become more powerful, so it never increases its
level or other abilities, nor can it regain expended spell slots.
Emphasis mine.
According to RAW, all of this means that the creature has all the statistics of the original, with the following differences:
- Half max HP
- No equipment (upon creation)
- Friendly to caster and those caster designates.
- In combat, acts on caster's turn and obey his wishes.
- Cannot become more powerful (earn levels).
- Cannot regain spell slots.
This are all part of the Simulacrum spell's ongoing magical effects: They are not part of "new statistics for the creature".
Then, from True Polymorph:
The transformation lasts for the duration, or until the target drops
to O hit points or dies. If you concentrate on this spell for the full
duration, the transformation becomes permanent.
Thus, also an ongoing magical effect.
And also:
Creature into Creature. If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge
rating is equal to or less than the target's (or its level). If the
target doesn't have a challenge rating). The target's game statistics,
including mental ability scores, are replaced by the statistics of the
new form. It retains its alignment and personality.
The target assumes the hit points of its new form, and when it reverts
to its normal form, the creature returns to the number of hit points
it had before it transformed. If it reverts as a result of dropping to
O hit points, any excess damage carries over to its normal form as
long as the excess damage doesn't reduce the creature's normal form to
O hit points, it isn't knocked unconscious.
The creature is limited in the actions it can perform by the nature of
its new form, and it can't speak, cast spells, or take any other
action that requires hands or speech, unless its new form is capable
of such actions.
The target's gear melds into the new form. The creature can't
activate, use, wield, or otherwise benefit from any of its equipment.
Emphasis mine.
According to RAW this means that the creature gets all the statistics of the original, with the following differences:
- Retains alignment and personality.
- HP of new form.
- Limited in action capabilities as the nature of the new form.
- Gear melds into new form
It is important to note that ongoing spell effects on a creature are neither part of it's statistics nor part of it's equipment:
Monster Manual page 6: STATISTICS
Note that ongoing sell effects are not mentioned anywhere in that section.
And MM 13 "Equipment" clearly lists only actual "physical" items, thus again no ongoing pure spell effects in there.
since True Polymorph says nothing about how it affects other ongoing magical effects, it means that they remain in effect normally.
So, for example if you cast the spell Haste on a human, and then True Polymorph hiim into an elf, the humans's gear melds into the new elven form, but the Haste magical effect is still there on the creature. This means that while the True Polymorph is active, the Simulacrum spell similarly doesn't just "go away", and remains in effect, too.
This means that all the listed effect, including limitations, from both Simulacrum and True Polymorph, are still in effect here:
- Half max HP
- Friendly to caster and those caster designates.
- In combat, acts on caster's turn and obey his wishes.
- Cannot become more powerful (earn levels).
- Cannot regain spell slots.
- Retains alignment and personality.
- HP of new form.
- Limited in action capabilities as the nature of the new form.
- Gear melds into new form
Now, the confusion seems to exist in the following aspects:
The combo now allows getting the full HP of new form.
No. Conflating CURRENT HP and MAX HP is a mistake. Even if an effect allows to keep full CURRENT HP, the "CURRENT HP is limited by MAX HP" rule still applies.
While it copies HP and MAX HP of the new form, the CURRENT HP is done as a copied statistic, which is then affected by the remaining spell effects: the ongoing magical limitation "Half MAX HP" remains in effect, dropping CURRENT HP to at most that specified half MAX HP value.
The combo now allows the creature to regain spell slots.
Again, while the capability to cast and regain spell slots is part of the "core" statistics that are copied over, this doesn't remove simulacrum's ongoing magical effect limitation that the creature cannot regain spell slots.
Make a comparison with Haste: what if Haste was caste on a human which is then Polymorphed into a horse... because a horse has a land Movement Speed statistic that is changed from human to horse by True polumorph, would it also suddenly means that the creature now lose the listed benefits of Haste?
No, the Haste listed effects are neither parts of the creature statistics, nor of it's gear, so you now have a horse with Haste. The Haste benefit is kept even though True Polymorph modified the exact same Statistic, namely movement speed. Similarly, additional effects from Simulacrum cannot suddenly "become ignored" when another spell is cast on the creature that "play with" the same Statistics.
A little bit that can help here is to not see spells as being "opaque overrides" that are cast "one on top of each other" like a pile, using only tihe" top visible" effect on any game statistic, but to see them all on an equal footing, and all acting together at the same time. So if spell A does an "Apply Limitation Y to the X Statistic" while spell B does a "Set X Statistic to the Value of Z Statistic", both effects will "try" to remain as much as possible. Thus, X is set to Z, but without suddenly ignoring the limitation that X is also suffering from the Y limitation.
Now, if Simulacrum's limitations to MAX HP and to regaining spell slots where described using a terminology that was like "At the instant the creature is created, apply these", in that case yes True Polymorph would allow "regaining" the full HP and spell slot regaining by casting it afterwards. But these Simulacrum spell effects are not written with a time-dependency like that, so they are applied constantly, in an ongoing fashion.