Does performing the assigned penance after confession remove all temporal punishment, i.e., is it plenary, remove all temporal punishment due to those sins just confessed but not others which we may have forgotten, or neither, i.e., can it be partial/inadequate (e.g., you murdered someone and you’re assigned 1 Hail Mary)?
I think you are confused here. When we go to confession we are most especially concerned with reconciling with God and having our eternal punishment (which relegates you to Hell) removed.
Confession: removes eternal punishment entirely, and the penance assigned here also can remove temporal punishment
Indulgence: removes temporal punishment partially (partial) or entirely (plenary)
Furthermore, there is a lot of overlap between confession/reconciliation and indulgences. For example, to receive a plenary indulgence you actually have to go to confession. If, while in the confessional, you tell the priest that you are seeking an indulgence, he can assign an indulgenced prayer or action as your penance. When, after leaving the confessional, you pray that prayer or do that action, you are killing two birds with one stone: penance and the indulgence.
It is really more helpful to understand indulgences and confession separately before trying to understand them together, because it can be confusing.
I suspected it’s not plenary. So there’s no necessary correlation between penance and satisfaction of temporal punishment? After penance, we may still have temporal punishment due to those sins confessed?
Confession makes sure you are invited to the Lamb's marriage supper. Indulgences have to do with whether you need to wash up first before you sit down to dine.
1459 Many sins wrong our neighbor. One must do what is possible in order to repair the harm (e.g., return stolen goods, restore the reputation of someone slandered, pay compensation for injuries). Simple justice requires as much. But sin also injures and weakens the sinner himself, as well as his relationships with God and neighbor. Absolution takes away sin, but it does not remedy all the disorders sin has caused.62 Raised up from sin, the sinner must still recover his full spiritual health by doing something more to make amends for the sin: he must “make satisfaction for” or “expiate” his sins. This satisfaction is also called “penance.”
1460 The penance the confessor imposes must take into account the penitent’s personal situation and must seek his spiritual good. It must correspond as far as possible with the gravity and nature of the sins committed. It can consist of prayer, an offering, works of mercy, service of neighbor, voluntary self-denial, sacrifices, and above all the patient acceptance of the cross we must bear. Such penances help configure us to Christ, who alone expiated our sins once for all. They allow us to become co-heirs with the risen Christ, "provided we suffer with him."63
The satisfaction that we make for our sins, however, is not so much ours as though it were not done through Jesus Christ. We who can do nothing ourselves, as if just by ourselves, can do all things with the cooperation of “him who strengthens” us. Thus man has nothing of which to boast, but all our boasting is in Christ . . . in whom we make satisfaction by bringing forth “fruits that befit repentance.” These fruits have their efficacy from him, by him they are offered to the Father, and through him they are accepted by the Father.64
and regarding indulgences: scborromeo.org/ccc/p2s2c2a4.htm#X
Does performing the assigned penance after confession remove all temporal punishment,
As a general rule, no, it is necessary to, and expect to do far more than what is assigned.