Hi 2 years before i did joined a company before my current companie notice preriod ended so 10 days moonlighting id in my work history now will it totally affect my career?

I had joined an IT organisation in sept 2022 and left it on 12th oct with immediate effect as they were calling me to Bangalore as they were ending work from home but due to genuine personal reason I was not able to relocate. And I joined another organisation on 12 th Oct itself as they had permanent work from home .but my previous employer kept on my paying me salary till December and given me last working day as December .so it has created an overlap of 2 months.so I am worried because If I approach my last employer they might not change the last working day in relieving letter. So my question is how should I Handle this situation after gettin selected in a new Company ? I don't want to showcase my employer which I left on 12oct on my cv but I will keep my new employer informed about it? Because they might come to know about later through UAN no and will it create trouble for me?

I have joined my next company as a contract worker while serving the notice period of first company ,I have received reliving letter from both the companies.Will this 2 month overlap of job will affect future prospects

So will this impact my future , when i apply for jobs will i be considered a bad candidate sir? I have zero knowledge about how market jobs works and this is depressing my like anything ? Please let me know the truth

Yes I have 1.9 years of work ex, and want to devote my full time to prep as I am weak in maths. If I quit now it will be 6-7 months gap till November. will it reflect very badly on my profile?