Regarding attending two programs simultaneously

There is nothing to be panic.
You are qualified in Polytechnic after 10th.
After completing your diploma you joined in B.Tech 2nd year by writing the entrance test and joined. Now you have completed your B.Tech.

You need not mention anywhere that you have studied 12th class. Even when you apply for your government jobs you need not mention your 12th qualification. You need not produce these certificates for verification at any place. Apply for jobs asking for the qualification of B. Tech or polytechnic. Then there will not be any problem.

Another important issue is you have done one course in regular mode and the other in private mode. There will not be any problem when you do like this. Doing two courses simultaneously in regular mode is not allowed. One course regularly and the other on distance mode or as a private candidate is always acceptable. You need not worry.

You need not think unnecessily on this point. You took up the diploma course on the basis of your passing class ten from a recognised Board. Later on the ground of your commendable performance in your Diploma course, you were inducted in the second year of the Engineering degree course.
Even your passing 10+2 privately is not likely to interfere any way since the prevailing rule states that no persual of two regular courses should be done simulteneously from the recognised institutions. In your case, there is no violation of any rule since you have passed 10+2 privately. However, to remain in safe side, it would be better to ignore your passing of class 10+2, while applying for any job in order to invite any complication.

You did absolutely right as per the rules. No need to worry about it. As you yourself mentioned that you have completed polytechnic after Class 10th in regular mode and did 12th class in private mode. As per rules you cannot obtain two degree or diploma simultaneously in regular mode. In your case your polytechnic diploma is in regular mode and 12th class through private mode. So no question arise of legal issue.

Further, as you have completed polytechnic in 2016 and then admitted to B.Tech lateral entry and completed B.Tech in 2019 itself. There is no need to show your 12th class qualification in academic qualification and produce certificate of 12th class while applying for any job. Show only polytechnic diploma and B.Tech degree for employment purpose.

And, I think if you will show your 12th class certificate anywhere they may not be any harm of doing so as it was done through private mode only. There will not be any problem due to your 12th class marksheet or certificate.

As per the UGC stipulations in this matter one can not do two regular educational courses simultaneously. At the same time if one course is regular and the other is private basis then it is allowed. So in your case one course was regular and other was on private basis. So you need not to mention this fact until unless you are specifically asked this question by the verification or interview taking authorities. Because of the UGC guideline people are not going for dual regular courses but many people are doing one regular and one private or correspondence mode course.

Hope this explains the situation to you clearly. All the best.