I checked through the train list and found the first train, 09268 PRYG-ADI express which has start date missing. The news section of the same train indicated that it started running post 25th March, as there are articles on 24th March saying that this train will be introduced by 25th. As expected, in many of the trains start date is missing because no one updated it.
See, generally on this site, we don't indicate start date on train list. There is a dedicated area on train page, called Inaugral date where it is shown. The reason is that the inaugural date of many trains, especially pre independence era ones is still shrouded in mystery and requires a fair bit of investigation...
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and poring over ancient timetables, old railway budgets, presidency Gazette of British and what not. Start date is indicated only for special trains as they run for set duration, and then stop running; normal trains are inaugurated once and continue running almost in perpetuity.
Currently due to the covid situation this mess has ocured involving special trains running as regular.
None of the special train will have start date earlier than may 2020, as that is when post the national lockdown first non-shramik all reserved special train started operations.

Third wave is expected around mid August, with peak in September, as per SBI report. They had correctly predicted the second wave and its peak almost to the week it hit.
We will see the same thing again, cases will go down, people will start clamoring for local trains/passengers (already happening in mumbai, commuters have threatened agitation if BMC does not allow normal passengers in locals, even though that is exactly how second wave began in Mumbai), offices and businesses will lobby using groups to ask permissions to open hotels, malls, office areas etc and the rest happens as per previous script.
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my office said no wfh after july, report to office in August beginning, and I know many with same situation.

On other hand, the true picture might be much worse.
Single dose efficacy with covidshield is quite low against delta variant. With two doses, the efficacy of covidshield is around 60%, the same figure for mRNA vaccine used in USA is over 85%. In india at the moment the percentage of people having both doses is around 5% only, and it isn't magically going to go up to 70 or so in next few months.
What should hopefully not happen as much is deaths due to covid.
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third wave, considering spread of vaccination and dose efficacy is almost inevitable.