The best refrigerator as a built in for me is the Sub Zero always has been but when doing the fully flush integrated look and if leaning towards a 42″ the Jenn Air is one of the few that will build in flush inset with the work of cleating the surrounding cabinetry.  That is a great option in  a french door.  Overall Sub Zero columns then Thermador for me.  Non built in the best option is the Fisher Paykel brand but they will come in a 36″ integrated so fully flush at a price point around $5000 . They do make columns as well but their 36 is a good hybrid approach.

What where you using to clean it with? there is an overflow valve on the back that if over suds could come from there. The clean cycle uses the highest volume and pressure of water so any compromised seals and on that cycle could def cause it as well and you would not see it on other lighter cycles. I would just use a normal cycle run some bleach through it once and a while. That will work well.

LF means there is a water issue and usually a kinked hose or clogged strainer but based on the fact you said there is water in the machine tells me your inlet valve aka solenoid valve is bad and needs replacing. When these go bad the first that happens is usually water fills in the tub as it doesn’t shut all the way off.  A bad valve will also throw the LF error code.

Induction is very reliable and a worthwhile investment. Thermador Freedom is a top pick of mine with the micro inductors it is very efficient and allows for place anywhere pan sensing technology. Kitchen Aid is probably the best value for a budget friendly induction unit as well.