The context here has to do with David's lust for more women.

And I gave you your master's house, and your master's wives into your bosom, and gave you the house of Israel and of Judah; and if that had been too little, I would moreover have given to you such and such things.

Please note the parallel to another previous passage:

^{Genesis 2:16-17} ¶And the LORD God commanded the man, saying: Of every tree of the garden you may freely eat: But of the tree of the knowledge of good and evil, you shall not eat of it: for in the day that you eat thereof you shall surely die.

As Adam before him was allowed to taste of the many trees of the garden of Eden, so also David was permitted to take unto himself wives from among the many unwed or widowed daughters of Israel; but, as the forefather of all mankind was forbidden to touch the tree of knowledge, lest he die, so also the ruler of all Israel was prohibited from touching wedded brides from among his people, lest he and his kingdom both perish, as it eventually happened, centuries after his time.

The context here has to do with David's lust for more women.

The context here has to do with David's lust for more women.

Not quite. The context has to do with sending someone to their death, so that one could then proceed to marry their widowed wife.

Just as anything ranging from simple theft to aggravated robbery is forbidden by the Mosaic Law, but the pursuit of wealth is not (provided that the poor, the widows, and the orphans are not forgotten, which constitutes a major theme in the prophetic books), so also adultery (in all its violent and non-violent forms) is prohibited as well, but the pursuit of (preferably virgin) wives (and concubines) is not. Of course, Christ does indeed explicitly and repeatedly condemn the acquiring of wealth in the Gospels, but He lived one and a half millennia after Moses.

I'm struggling with a verse that seemingly supports God's approval of concubinage and taking of many wives. [...] This makes me feel uneasy leaving this lingering in my mind.

Does God's tacit or implicit tolerance of polygamy make you feel uneasier than Him explicitly commanding that various types of (sinful) people be put to death by stoning, or that entire cities, including their (male) children, be blotted out of existence ? If you accept the latter as biblical fact, why not the former as well ?

Or perhaps you are simply bothered by the fact that the Gospels contain no polygamy-related equivalent of John's Pericope Adulterae, explicitly condemning the practice ?

Is to be interpreted as approval of polygamy or is the main focus something else ?

As already mentioned above, the Mosaic Covenant does not forbid polygamy; were that not the case, then there would have been no logical reason for the Prophet Nathan not to explicitly mention this to David as well, just as he explicitly mentioned his (indirect) murder of Uriah (in a manner not explicitly forbidden by Mosaic Law; after all, it's hardly a sin for a king to send his most trusted and valiant fighter into battle) so as to legally take his widowed wife as his own, since adultery, unlike David's conniving plot, was explicitly forbidden by the Law.

• As the Pharisees after him, David kept the letter of the Law, while breaking its spirit, by infringing upon its intended purpose and meaning.

• As Christ in New Covenant times, Nathan the Prophet is tasked by God to remind him of that.

Is to be interpreted as approval of polygamy or is the main focus something else ?

The main focus is (obviously) obedience to God's law, and trust in His divine providence.

Did he desire (yet) a(nother) wife ? If so, then why not acquire one by then-legal means, having faith that the same God that delivered all other blessings into his hands will not fail him this time either ?

The context here has to do with David's lust for more women.

Not quite. The context has to do with sending someone to their death, so that one could then proceed to marry their widowed wife.

Just as anything ranging from simple theft to aggravated robbery is forbidden by the Mosaic Law, but the pursuit of wealth is not (provided that the poor, the widows, and the orphans are not forgotten, which constitutes a major theme in the prophetic books), so also adultery (in all its violent and non-violent forms) is prohibited as well, but the pursuit of (preferably virgin) wives (and concubines) is not. Of course, Christ does indeed explicitly and repeatedly condemn the acquiring of wealth in the Gospels, but He lived one and a half millennia after Moses.

I'm struggling with a verse that seemingly supports God's approval of concubinage and taking of many wives. [...] This makes me feel uneasy leaving this lingering in my mind.

Does God's tacit or implicit tolerance of polygamy make you feel uneasier than Him explicitly commanding that various types of (sinful) people be put to death by stoning, or that entire cities, including their (male) children, be blotted out of existence ? If you accept the latter as biblical fact, why not the former as well ?

Or perhaps you are simply bothered by the fact that the Gospels contain no polygamy-related equivalent of John's Pericope Adulterae, explicitly condemning the practice ?

Is to be interpreted as approval of polygamy or is the main focus something else ?

As already mentioned above, the Mosaic Covenant does not forbid polygamy (Moses himself, through whom the Law was given, had multiple wives, as explicitly mentioned in Scripture); were that not the case, then there would have been no logical reason for the Prophet Nathan not to explicitly mention this to David as well, just as he explicitly mentioned his (indirect) murder of Uriah (in a manner not explicitly forbidden by Mosaic Law; after all, it's hardly a sin for a king to send his most trusted and valiant fighter into battle) so as to legally take his widowed wife as his own, since adultery, unlike David's conniving plot, was explicitly forbidden by the Law.

• As the Pharisees after him, David kept the letter of the Law, while breaking its spirit, by infringing upon its intended purpose and meaning.

• As Christ in New Covenant times, Nathan the Prophet is tasked by God to remind him of that.

Is to be interpreted as approval of polygamy or is the main focus something else ?

The main focus is (obviously) obedience to God's law, and trust in His divine providence.

Did he desire (yet) a(nother) wife ? If so, then why not acquire one by then-legal means, having faith that the same God that delivered all other blessings into his hands will not fail him this time either ?