Well, I had to leave the chat after spending a long time on it, with the intention of resuming when I had more time. Today I decided to take matters into my own hands once more. I did all the old stuff — first disconnecting and reconnecting just Safari from iCloud on both devices, then disconnecting and reconnecting from and to iCloud altogether. At that stage, syncing even of Contacts and Calendar became erratic, especially so from phone to Mac. I then disconnected and reconnected iCloud fully once more, but this time I took what seemed to me a risk and chose the option (on both devices) of not keeping copies of data on the devices (except for passwords), but hoping that I would be able to restore all my data from iCloud.
When I reconnected, I was (after some difficulty and after repeating part of the procedure yet again) able, to my great relief, to get all my data back onto both devices, but syncing of everything was still erratic. I was about to give up and try a chat with an Apple advisor again, when suddenly everything started working and bookmarks synced, too.
Maybe the problem had in fact lain with iCloud.com? I had in fact checked the service status and it had appeared to be OK, but maybe it was somewhat intermittent. Whether the problem will recur remains to be seen. And because of the complexity of syncing to and from two devices in several applications and the apparently erratic nature of the misbehaviours, I am not sure whether my repeated logging out and back in to iCloud was what repaired the situation, or whether it was indeed a temporary phenomenon at iCloud.com. In the meantime, I (fingers crossed!) am greatly relieved that syncing of bookmarks as well as of Contacts and Calendar seems to have been restored. I shall continue to keep an eye on it.