The transactions in image 2 show you the transactions that were sent. Literally setValue(25), from/to, UID (transaction Hash), block number where it was mined, etc. - but not the effect. The answer you seek is not there.
Up above, where you did app.getValue() you got the value at the time. That is how you inspect the contract state via the function in the contract.
What is throwing you off is the format of the response. The contract uses a 256-bit integer and JavaScript has no Type for that. Instead, what you get is cast as a BigNumber using the BigNumber.js library (rolled up into Web3) that organizes the significant digits in a special kind of object and gives methods for math operations.
This is the case with all uint responses.
You can go:
$ let x = await app.getValue()
$ x
BN: { <bigNumber object> }
$ x.toString(10)
`25`
This prints the value of x, a BigNumber as human-readable string interpreting it with the base-10 number system.
A best practice is to get used to casting all of your "big numbers" this way and performing your math operations with the BigNumber methods. This way, you won't lose any precision. Then present the human-readable format through the UI. For example:
let x = await app.getValue(); // returns a BN
let y = web3.utils.toBN(`1`); // cast `1` as a BN
let z = x.add(y); // add two BN returns another BN
let zReadable = z.toString(10); // human-readable string, not recommended for math
console.log("The next number in the sequence is", zReadable);
Hope it helps.
