The half notes should sound their duration and form a line of their own. The question is how to achieve this. If you use the dampener pedal, all no longer struck notes will get finished in the same manner.
Now the shorter figures in the bass have their own character and are somewhat independent with their overlap and individual capacity of being cut off by unpedaling. The other treble notes form melody lines where each sustained note is followed by an adjacent note, so the basic "attention" moves on.
That makes the question important just how you are going to end the sustain. Letting the last note of the melody and bass lines stand out when unpedaling does not make sense, so the unpedaling action should be rather brief.
That means that your long notes are probably fine being held just with the pedal. However, you want to let them keep some basic weight over the accumulating sustained notes, so it would be good if you manage to strike them more distinctly/louder than the simultaneously starting "shorter" notes that are actually sustained just as long.
So just to get a bit of a feeling for the long notes: if you have the skills required for holding the long notes while playing onward without needing to practice a lot, it may make some sense to try at first not pedalling at all and playing as written, just to get a hang of the voice leading you want to have more or less in the end.
It might also be possible to strike the long notes slightly before the shorter ones (so basically the reverse of the written order) to have them stand out with a slightly different point of articulation while not then interrupting the faster line. You need to try it out to see whether this works in your desired speed and interpretation.
Basically when you record the result, it should sound like what was written: consider the score a hearing rather than a playing instruction.