I'd like to look at this from a couple of different angles (for a reason).
(1) The RH has phrases that singers would sing, and singers breathe. The rest is the spot between phrase where the singers grab a breath without being late at the next beat. Picture the "Happy Birthday" song and you'll hear that little pause: if you picture it without those pauses it would sound strange. At the end everyone seems to let that last "you" go on maybe a little too long because they're amateurs having fun - but it indicates the instinct we all develop to have a kind of longer "the end feel" to the end of music. This is likely what is going on. If you were an advanced musician, you'd likely make at least a little bit of a break between phrases, and the break (rest) might be shorter or longer than that rest value. If the last notes in m. 4 were written as dotted quarters, the advanced musician might still put in some kind of a "breath".
That's the main thing. I saw one person on YT refer to "Clara Schumann's edition" stating that this was the one he was using, so there might indeed be various ways this is notated. The other factor being that these are supposed to be pieces for learners, so there is the question of how to present this to learners.
extra thots;
(2) We also have the context of where this music appears, since there are instructions on top. Is this a teaching series? (Maybe Canadian edition, given the usual bilingual text). So at this stage they seem to be stressing note values, some aspects of touch to help you, and they may be introducing or stressing 6/8 time with its two pulses/measure. You'll be following the instructions rather literally, and to a degree you need to. But also allow your musical sense to jump in for the sense of some of it.
I'm seeing that this is usually played with pedal, and pedal is indicated in the original notation. If pedal hasn't been taught, that's a reason not to have pedal in the music (ofc). The presence of pedal would change how long your fingers actually hold down the notes. The LH, for example, might be the touch of an eighth note because the pedal holds the notes for their full value. The last notes in m. 4 would be released early even at the end, and you'd make it last shorter and longer by your pedal release. That also makes the RH easier to play since you'd not have to hold down the bottom notes while playing the top voice.
