It's makes it harder because of the way your ex has gone about things.
He hasn't known his partner very long at all, especially in view of lockdown, but is planning a wedding and buying a house. She will quite probably have heard the story of how he split from you because he was cheating. He was with the other woman, but then that split up. Because she doesn't know him well enough to make sense of all this and his rationale towards life, there is quite a possibility that his new wife will be rather jealous, and given his history of unfaithfulness, and love of romance, that jealousy will be intensified. She might be jealous of you, because you have been on days out, etc., with him, and she might - as you say, wrongly - think that there is more between you. You have a bond with him, because you share kids; she doesn't yet have kids with him, so that might make her jealous. Friendship can arouse jealousy more than the fear that a partner fancies another woman. You might be the only woman who has stayed in his life and held his regard for the longest. She must be very keen on him to be settling down with him after so short a time and knowing about his eye for the ladies.
I would imagine that you are doing what you can to make things nice and pleasant for your shared children. I wish that he had given it more time with this new partner, before formalising their relationship with a wedding, so she could get to know you and realise you are not a threat, and so that she can get to know this side of his life and his children. It will be easier with giving the kids great times, if you can all get along. I think it would be good to talk to him now and to express some of your feelings and ask him what he thinks she will accept as a tolerable measure of your friendship. Some people seem easygoing, but change once they are married, and she might be like that. I would express any misgivings you have, but in terms of his contact with his kids and keeping this regular.- which is the thing which matters.
As you have got on with your ex, chatted and met regularly, access arrangements for the kids may have been informal, to date. It may be good to firm these up to set days, because his new wife will want to have the major say in what he does with his time, and it would be ideal if the marriage would start with them understanding that certain days are his time for the kids.
The main thing is the happiness of the children, so be prepared to pull back in order to lessen any suspicions and just work to make his contact with the kids easy and frequent.