In one word, no. The modules you used are not intended to be connected together like that to make the circuit you want. The problem is battery output being consumed while it is charging.
Passing UL or CE is a completely separate subject from having a circuit that does something properly.
And since passing UL or CE is also about how the PCB mains wirings are done, so it's a bit early to ask that as there is no PCB design to see if it passes UL or CE.
So even if you could pass CE or UL with that circuit, it is still a circuit that does not do what you want it to do, at least not correctly or in a good way.
First of all, you are putting together modules. Now, we coul guess what modules those are and what they do, but we don't. So they are unknown black boxes and it is unknown what they do and if they can be connected like that.
Then if we start guessing, the TP4056 module is a lithium charger module, and such modules may aready contain a BMS.
Then you have a separate BMS whose parameters are also unknown.
And then you have an unknown lithium battery cell which might also contain a BMS.
And for the TP4056 chips you cannot have a load on the battery while the battery is charging. Otherwise the TP4056 cannot detect early enough that the battery is full and it keeps the battery on float charge for too long, always and each time you charge the battery. The charging may never end because of this and the battery is constantly being float charged.
And lithium batteries cannot handle being float charged constantly. Incorrectly handled lithium batteries will degrade and damage and damaged batteries are dangerous as they can explode or burst up in flames and start a fire.