Your charger circuit has a couple potential problems, depending on the load current at your LDO. The TP4056 terminates charging when the charge current drops below 10% of the full charge current set by Rprog. If your load current is greater than that, charging will never terminate, which is bad for the battery, and possibly dangerous. However, if you can periodically put the ESP32 to sleep, and bring the load current below the 10% level, then termination should take place properly. Even so, if termination does occur properly, you then have the battery powering the load when the solar panel could be doing so - the charger has shut down.
The solution to these problems is a load sharing circuit, which lets the panel directly power the load whenever it's illuminated, and charge the battery independently if needed. But load sharing for a solar-powered TP4056 is complicated because the solar panel voltage is variable.
But if your battery is 200mAH, you'll have to change Rprog anyway so the max charge current is 200mA, or perhaps 100mA. But note that the bigger the battery, and thus the greater the charging current, the easier it is to get load current below the 10% level.