everyone certainly has different opinions in this matter, but in my opinion, using emergency funds is certainly free to do at any time if for example we are pressed for medical expenses and so on, as long as the most important thing is that we don't sell btc because the function of emergency funds is so that we can hold btc for the long term and so that when we invest in btc it remains comfortable. and it would definitely be better if we could add emergency funds every month or whenever.
yes, hopefully all of us who invest in btc and do dca will be given health and kept away from danger and hopefully our income will increase so that when we invest in btc we will be calmer.

I am concerned about your statement. You are free to express your opinion and use your funds at any time, because they are yours alone. But this statement may be a bit confusing for the inexperienced. Because, using an emergency fund at any time may not be the right move.
As you mentioned, an emergency fund can be used at any time and it would be better to re-deposit it at the end of the month. Would this actually be a good move? How reasonable is it to use an emergency fund without an urgent need and how will such a quote affect a beginner? What kind of plan would you work with if an emergency arises at the very moment of using an emergency fund without an urgent need? I can't see any way other than taking out a loan or selling BTC.
So it might be a good move if you don't use the emergency fund in the initial stage of the need and keep the emergency fund safe as long as you can. Then you use the emergency fund, but if the emergency does not end, you blame fate. Because you have been fighting the emergency for a long time and have not won. So plan to fight the emergency for as long as possible. By putting your hand in the emergency fund at the beginning, you are putting your hand in the main weapon at the initial stage of the fight.