Reading the wikipedia entry on High Crimes and Misdemeanors probably suffices to answer the question. Ultimately this phrase doesn't mean what you think it means. Your modern notion of "crimes" and "misdemeanors" is not what is meant. It comes from England, with hundreds of years of history behind it. In short it (probably) means "anything outside of or contrary to the usual norms of governance", which effectively means "anything you can get enough votes for". It is the political practicalities which end up making it a seemingly very difficult thing for a President to get convicted of, rather than its actual scope and meaning.
Some choice quotes from the article:
Since 1386, the English parliament had used the term “high crimes and misdemeanors” to describe one of the grounds to impeach officials of the crown. Officials accused of “high crimes and misdemeanors” were accused of offenses as varied as misappropriating government funds, appointing unfit subordinates, not prosecuting cases, not spending money allocated by Parliament, promoting themselves ahead of more deserving candidates, threatening a grand jury, disobeying an order from Parliament, arresting a man to keep him from running for Parliament, losing a ship by neglecting to moor it, helping “suppress petitions to the King to call a Parliament,” granting warrants without cause, and bribery. Some of these charges were crimes. Others were not. They can be thought of as serious cases of power abuse or dereliction of duty, without a requirement for these cases to be explicitly against the law.
Benjamin Franklin asserted that the power of impeachment and removal was necessary for those times when the Executive "rendered himself obnoxious," and the Constitution should provide for the "regular punishment of the Executive when his conduct should deserve it, and for his honorable acquittal when he should be unjustly accused." James Madison said that "impeachment... was indispensable" to defend the community against "the incapacity, negligence or perfidy of the chief Magistrate." With a single executive, Madison argued, unlike a legislature whose collective nature provided security, "loss of capacity or corruption was more within the compass of probable events, and either of them might be fatal to the Republic."
The available records we have from the era of the writers of the constitution gives the clear impression that none of the things that qualified as "high crimes and misdemeanors" actually had to be a crime. Frequently they weren't. They were instead concerned more with things like abuse of power, betrayal of the public trust, ineptness, etc.
But some legal scholars do adopt a more stringent interpretation, saying it is only meant to cover the most severe of possible actions, including Bill Clinton's lawyers during his impeachment. In 1999, following Clinton's impeachment saga, Mark Slusar argued this more stringent/narrow interpretation was the prevailing opinion among scholars and Senators.
In practice to date that's at least been how things have panned out, as no President has ever been convicted in the Senate and only two have ever been impeached by the House (Nixon resigned before that happened, and it hasn't yet happened to Trump, though most expect it will, and soon). But no court has issued a binding opinion on what the term means for a Presidential impeachment.
Finally, note that many Democratic talking points are now emphasizing the "bribery" angle, which is specifically noted as cause for impeachment, in addition to high crimes and misdemeanors, in the Constitution. This has the benefit of not suffering nearly as much from the ambiguities of old English common law terminologies having diverged from modern terms, or the corresponding disagreement on what the correct constitutional interpretation and application of them is. It may be easier to think of your not-so-hypothetical as an instance of bribery, rather than of "high crimes and misdemeanors".