The more you pay, the more features you'll get, so it makes sense that the most expensive of the cheap air purifiers does in fact have the most smarts too. Ikea's Starkvind air purifier, which retails for $199, or $249 inside a table is compatible with Ikea's Home Smart app.
Within the app you can see detailed air quality readings, set timers and schedule operations, and do it all remotely. Unfortunately this functionality isn't entirely baked in. You'll need to purchase a Dirigera smart home hub for $99 to be able to access all these smart functions. That does bring the total cost of the device up to at least $299, which is still cheap for an air purifier but expensive for one without HEPA filtering.
Another good option is once again Kmart's Large Air Purifier which has timers, a 30-minute auto-off function, and a remote control. Couple it with a smart switch and you can somewhat replicate the functionality you'll get with Ikea's app.
Notably, none of the models across either brand have air quality readouts. Usually air purifiers use a simple traffic light system to indicate whether air quality is excellent, good, or awful. Even at its most basic this at least lets you make informed decisions about how fast you need to pump your purifier. Ikea somewhat circumvents this by offering the Vindstyrka air quality sensor for $59 which can be connected to a Starkvind, or the less sophisticated Vindriktning for $19 to go with the Fornuftig. The Vindstyrka displays PM2.5 readout, the room temperature and humidity, and if the total volatile organic compounds are increasing or decreasing.