The need to keep track of STT per trade arises when you are reporting the gains/losses from your transactions as capital gain/loss . If you are reporting this as business/speculative income and not as capital gains/losses, then you may not have to keep track of this. I have never had to do this latter thing till now, so I am not sure about the reporting requirements when it comes to noncapital gain incomes/losses from shares.
If you are reporting capital gains or losses from buying and selling shares, then you do have to know how much STT you paid on each trade. This is because we are, somewhat counterintuitively, not allowed to discount the STT paid, from our gains. That is, suppose we do the following trades (all numbers madeup):

Bought 1000 shares of INFY on 01Jan2019 at a market cost of Rs.1000 per share. Paid Rs.1000 as brokerage, Rs.500 as stamp duty, Rs.200 as sundry charges and taxes, and Rs.1000 as STT.

Sold the above 1000 shares of INFY on 01Aug2020 at a market price of Rs.1500 per share. Paid Rs.1000 as brokerage, Rs.500 as stamp duty, Rs.200 as sundry charges and taxes, and Rs.1500 as STT.
Then the total money that we spent on acquiring these 1000 INFY shares is Rs.(1000x1000 + (1000 + 500 + 200 + 1000)) = Rs.1002700. And the total money that we got by selling these 1000 INFY shares is Rs.(1000x1500  (1000 + 500 + 200 + 1500)) = Rs.1496800. So the net profit we madeâ€”the actual amount or rupees that we have extra in our account, because of this pair of tradesâ€”is Rs.(1496800  1002700) = Rs.494100. And 10% of this is Rs.49410, which is the marginal amount of tax that we assume we have to pay on these gains.
But for computing LTCG we are not allowed to write off the STT that we paid, as part of the cost of buying/selling. So we have to report these numbers as: total cost = Rs.(1000x1000 + (1000 + 500 + 200)) = Rs.1001700 and total amount realized = Rs.(1000x1500  (1000 + 500 + 200)) = Rs.1498300, so that the total capital gains is Rs.(1498300  1001700) = Rs.496600. And the marginal tax on this is Rs.49660, which is more than what we found in the previous paragraph.
(Note that all the above numbers are bogus; my point was only to illustrate that not discounting STT has an effect in the tax liability, and so I didnâ€™t put in any effort into making the numbers realistic. )
If we are to compute the tax liability correctly, we need to know the STT that we paid on each leg of the transaction. If you did 10 transactions (say 5 buy, and 5 sell) on 01Jan2019, 15 transactions (say 5 sell, 10 buy) on 01Aug2020, and Zerodha only tells you the total STT that you paid on each of these days, then you will have some real fun trying to keep track of the various STT amounts to add/subtract when doing the filing.