Here's an excerpt from 明鏡国語辞典 第三版:
こ・む【込む・混む】[動五]
❶【混】ある場所に人や物などが集まって、いっぱいになる。混雑する。「通勤通学で電車が混む」「車で道が混む」「客で行楽地が混む」
❷【込】行動の予定などがぎっしり詰まっている。「日程[予定]が込んでいる」
❸【込】勝負事などで負けが重なる。「負けが込む」
❹【込】仕組みや細工が複雑に入り組む。「手の込んだ仕事」
◆書き分け
①は「込む」とも書くが、今は「混雑」をふまえて【混】が一般的。②~④は【込】を使う。
So this suggests that these こむ are basically the same word, but the kanji 混 is now the default choice when the verb means "(for a place) to be crowded".
Personally, I always prefer using 混雑する in writing to avoid any arguments. If I have to choose between 混む and 込む to express "crowded", 混む is much more common and safer in contemporary Japanese. 込む might be perceived as old-fashioned, or in worse cases, it could be taken for a typo.
EDIT: In BCCWJ, there are 1,670 examples of 込んでいる. I checked the first 200 of them, and found that only one of them meant "crowded" (the remaining 199 were false positives like 読み込んでいる and 考え込んでいる). On the other hand, there are 112 examples of 混んでいる, all of which mean "crowded". These objective results suggest that 混んでいる is several dozen times more common than 込んでいる in modern Japanese, and this perfectly aligns with my personal experience, too. It's safe to say 混んでいる has now become the norm regardless of its history. We shouldn't fall into the etymological fallacy.
EDIT 2: The 1981 jōyō kanji list and dictionaries from the early Showa period do not include the kun-reading 混む, but this reading was added in the 2010 revision of the jōyō kanji list, along with other super-common readings like かなめ (要) and わたし (私). As evident from the real usage examples in the BCCWJ, 混む has been overwhelmingly more common than 込む since the postwar period. Thus, the standard appears to have recognized the actual changes in the language.
EDIT 3: I also checked the results from 青空文庫全文検索 that mainly contains prewar novels. Since Japanese was not as standardized back then, there are some examples that seem unnatural from today's perspective, but the overall trend is almost the same as that of BCCWJ. The vast majority of authors, including 宮沢賢治, 谷崎潤一郎 and 太宰治, use 混んでいる for the meaning of "crowded". This suggests that 混む is not a "recent misuse" but a perfectly valid kun-reading that has been around at least since the era of the genbun-itchi but was omitted from the jōyō kanji list for some reason. We know of a similar example.