How to stand up for yourself professionally without being dominating ?

So It has been close to an year since I have been promoted as a Technical Lead (Android) and I am really struggling with how to establish the fact that I am at a certain position after I have worked very hard for it and that you need to have a certain level of respect while talking to me .

The people I work closely with do respect my opinion and my work . But, whenever there is a cross team interaction (including VPs ,Product and Engineering Managers ) mostly my Engineering Manager is the one who discusses or answers things , but when he is not available I am the one who would be pulled into these meetings and then I often face these intentional and indirect way of dismissing my opinion .

So for example , Just recently I was in a meeting and I raised a specific case that needs to be considered and even though I was right , The product head from my team started saying that it's not the right solution and I started answering him (which was a mistake since he didn't know the flow and was probably trying to be heard or to show that he is participating, he has also tried to somehow degrade me in discussions earlier but wasn't successful since he is new and doesn't know the application features very well ) . I said something along the lines that we may be getting distracted from the main discussion here , and then this is what happenned :

One of the senior management head told me " Can you repeat what you just said ? "

Me : I think we can discuss this later on to give more context to AP(Product head)

Senior : No what you said in the end ? I couldn't hear it , can you repeat ?

Me : "No I was just saying that we were probably heading in the wrong direction? "

Senior : Right , I agree , Let's move ahead .

I know it seems like a small thing , but I strongly felt like it was intentional as if he was irritated with me and wanted me to feel that I was just wasting everyone's time .

One of the VPs later on connected with me to understand what I was saying and he said that It was a valid point and we discussed the way around .

It was really humiliating to the core and this has happened with me a lot that I am explaining something and then one of them would say , Can somebody explain this in Hindi and then he would ask my Manager to explain even though I have been told that I explain things very well in multiple meetings with Engineering Managers from different teams who are genuinely professional and respectful so I don't really think that that's the reason they behave in this way.

I have discussed this behaviour with my Manager and he told me that they do behave like this sometimes and that I should just answer only what has been asked to avoid such instances if he isn't in those meetings .
I am generally very soft spoken and helpful, assertive(but not dominating I don't personally believe that's a good way to lead) , also , I manage things pretty well as per my designation . But incidences like these just make me feel how do I navigate from somebody who is helpful , well behaved but also to somebody who people don't dare to talk to in this way ?

Sorry for such a long post but It would really help me if someone who has transitioned from an SSE to Tech Lead and has faced similar circumstances or have observed someone going through the same on how to standup for myself without a literal fight ?