Oh dear I can see why you feel discouraged.
Well, it's your call at the end of the day.
I wouldn't have started with peas as they have to be pureed to prevent them being a choke hazard, but then pea puree has a bit of a weird texture don't you think, or is that just me thinking that?
I wouldn't have thought it any harm to offer a finger food to suck, lick, gum as you did with the cucumber over those 2 weeks but obviously I am not a paediatrician. There are such varied thoughts on weaning I feel that parents need to inform themselves and make their own choice. When my LO was 6 months I went on a weaning course run by the local health visitors and whilst I listened intently I disagreed with what was said and made my own mind up (in essence they said BLW was dangerous but also said puree stage lasted only 2 weeks and finger foods had to be introduced at 6 months - I couldn't work out how one was described as dangerous and the other advised as best practice when they were both finger foods. In other parts of the UK at the same time as this HVs were giving advice to go the BLW route and no purees...such varied advice).
I do agree that introducing green food earlyish can be helpful as it gets LO used to the taste.