The option to play the Sims archives does not show up for any sim with any computer. The option to research shards of time is blocked by "this sim is locked from using this computer" for all Sims on all computers. I've repaired the game tried different Sims from the same house, the same save and a whole new save.
It may be caused by a mod. Try removing your mods and see if the issues remain. With the play the Sims achieves task, you first need to click on play game, and then play the Sims archives.
I did take out all of my mods. The option for Sims archives does not populate under the play game option.
Are you playing in an apartment ? That seems to give all kind of issues. If you do, try going to the library and try the computer there.
Not an apartment and I've tried at the house and library
