The 21-year-old made his professional debut against Benetton at Scotstoun in March, marking the occasion with a try and a Player of the Match performance.
For Watson, the achievement also carried extra significance through his family connection to Scottish rugby.
His grandfather, Bill Watson, won 10 caps for Scotland during the 1970s, lining up alongside the likes of Andy Irvine, Ian McLauchlan, Jim Renwick and Sir Ian McGeechan before later serving as Chief Executive of Scottish Rugby.
"Growing up and seeing his cap and wearing it, I was like, 'I want one of those one day'," said Watson.
"My mum and dad worked quite a lot, so we spent one or two days a week with my grandparents, playing in the garden and whatnot. He's been to most of my games, followed most of the journey.
"He gave me a handshake and a 'well done' after my debut. He had a bit of a look in his eye and I understood what he meant. As long as I keep making him proud, I'm doing something right. For him to be there in that moment was pretty special, to get my family in the changing room and see the jersey presentation.
"We were looking back at old match programmes recently and they had the weights of the players recorded in them. Comparing that to nowadays, I would have been one of the heaviest players there. My granddad was just saying how much the game has changed. When I go home and sit and watch rugby with him, it's quite interesting to hear his interpretations and he is asking me things as well."
The family connection has also produced some memorable moments during Watson's development.
During his first week with Scotland U20, Watson was approached by forwards coach Fergus Pringle, who had previously worked under Bill Watson at Boroughmuir.
"He came up to me and asked, 'is Bill Watson your grandfather?'.
"'Yeah.'
"'I'm pretty sure he fired me from Boroughmuir.'
"Oh, well that'zz a great start."
Watson's Glasgow debut jersey was presented by Josh McKay, with the pair having worked closely together as members of the Warriors' back-three group.
"I remember first coming in and Josh was one of the first guys to speak to me, come up and shake my hand," said Watson.
"Being in the same position, he was always really approachable. I could ask him anything and he always had time to give me an answer. Even now, in the gym, he's having banter with us.
"He told me not to dwell on mistakes and when you do something well, he'd make sure you knew. Even on my debut he told me to go out there and have fun, and he'd give me the ball. It liberates you from pressure knowing he's got your back."
After making two appearances for the Warriors in 2025/26, Watson was invited to train with Scotland's senior squad during the summer Nations Cup campaign.
"I've done it in the Six Nations where you go in for the day but to be in that environment and be accepted by the other boys - I kind of felt because I'd played this year, I had a bit more respect.
"A lot of the Glasgow boys were in as well, so I was able to have a bit more banter which made me feel more comfortable on the pitch and express myself. You can just see it's a step up but it doesn't seem crazy far away."
Watson has also highlighted the contribution of Glasgow Warriors Academy Strength and Conditioning Coach Luke O'Dea to his development, having worked extensively on his strength and conditioning since joining the club's pathway.
"I've been able to lift weights I never thought I'd be able to. He was the real turner for me, making sure we were hitting targets but in the right manner. I could speak to him about anything. That's what he instilled. He's one of your mates rather than your coach. Even when it got tough, you are getting absolutely flogged, and we are in the red bib team training against the main team, it's good to have a guy in your corner."
Having featured at full-back during Glasgow's pre-season fixtures against Newcastle Red Bulls and Bath, Watson is now targeting further opportunities during the 2026/27 campaign.
The back-three player believes his carrying game remains one of his key strengths, while continuing to work on other aspects of his game.
"I'd say my ball-carrying ability, beating defenders, that's my super-strength," he said.
"My aerial game, trying to be a presence in the air and win the space as well as the ball with the way the game is evolving. The high ball as we saw over the All Blacks-Springboks games recently, they've really gone after that and that has really defined who is going to win. I need to keep pushing that. I'm trying to work on my kicking game as well. Maybe not so much at wing but if I'm playing full-back, looking for those corners.
"And also defensively, trying to put myself in trickier, uncomfortable positions and seeing how I cope with that. Scott [Forrest, Glasgow's defence coach] is really good at helping us with that, making us be brave, testing your height and width in the defensive line."
Watson is part of a group of young players who have progressed through the Warriors pathway together, with several making the step into the professional squad ahead of the new campaign.
For Watson, the opportunity to continue that journey alongside familiar faces is something he is enjoying.
"To be able to come into work every day and it's with your pals, and on the weekend there to be playing with all the boys, it's real good fun.
"It's so good for them to all be signing as pros too, I'm so happy for them because it wouldn't be the same without all of them. I'd have met guys like Johnny Ventisei and Matty Urwin when I was 16, and to come all the way through with them was pretty special. To share the pitch with them in a URC or European fixture would be cool."