What is your definition of cheap? I think for a new big name and or Western brand you are looking $5500-$6000 range bare min for an entry level aero, electronic, integrated bike maybe $5K if you go cheaper foreign frameset. Like others have said buying a frameset can create a bike that better fits you and your budget just know there really aren't big name or Western brands that sell "aero" framesets for anything less than $2800 starting.
With this being said I know someone people will think I am some China shill and give me flack for this but if OP really wants the cheapest well made modern aero bike on a budget than frankly I'd said just buildup a Winspace frame with Rival AXS, albeit it will be pretty heavy. My favorite local store is Brands Cycles in Long Island NY but they have a great online shop. They have Rivals AXS on sale and with a full groupset w/ the left side power meter upgrade kit, bottom bracket, tape, TPU tubes, Tires GP5000, Force chain, and cassette comes to $1814 before taxes. Winspace Summer sale has the last gen T1550, bars, and Hyper D45 SE wheels for $2821 shipped, thus in practice OP could have a modern aero frame, with aero wheels, fully integrated cockpit, fully wireless 12 speed groupset with power meter for $4635 before assembly or taxes. Factor is a $350 build fee at a LBS and OP would have a $5K bike before taxes. I would say in years past this would have been an amazing value and really the ONLY thing that gives me pause is Canyon's current sale for:
Aeroad CF SLX 7 eTap
$5100
https://www.canyon.com/en-us/road-bi...farbe=R081_P08
Aeroad CF SLX 8 Di2
$5400
https://www.canyon.com/en-us/road-bi...farbe=R081_P08
Aeroad CF SLX 8 AXS
$5700
https://www.canyon.com/en-us/road-bi...farbe=R081_P10
IMO the Canyons are simply better value for marginally more money considering you don't need to source parts and build up a frame however it should be asked: does the Aeroad geo work for you? Do they have your size in stock? Do the components in your desired size work for you, ie cranks, saddle, and cockpit length and width with 39cm being the smallest width? Are you okay with possible seatpost slippage and really no LBS support? For me personally these are amazing prices for a top notch aero bike however I do think the newly released updates for the current gen Aeroad like with Canyon selling the Pace bar sold separate so you can actually get your desired stem length without having to trade or sell your original cockpit with randos online is amazing. I think the optional Pace aero drops having the ability to go as narrow as 35cm width are amazing and frankly should have come standard. I think the fork protection and providing a TX25 thru axle tool are both cool. I also think the supposed added rear stiffness is also great. This is to say I think the "New" aeroad SLX 7 either 105 Di2 or Rival AXS are the better bikes to buy at $5600 granted that $5600 is a bit misleading since it doesn't include the $100 shipping, I personally would need a large Pace stem at $200, and I would want the more narrow and aggressive Pace aero drops at $230. Basically the cheapest "New" SLX 7 really is $6130 before tax and since the whole cockpit need to be reset up and rebled I think bare min you are looking at $70-$150 at a LBS or just the hassle of doing it yourself