Does Guild Wars 2 have micro-transactions that give competitive advantages?

No, GW2 is not a "pay to win" game.

Microtransactions in GW2 are made with an in-game currency called Gems.

Gems can be traded for gold or spent in the Gem Store. This means that anything that can be bought using only in-game gold can essentially be bought using real-world money. This would be problematic in games where having the highest stats is rare, but achieving the best stats in the game is common in GW2, even among casual players. Expensive items are typically those with the rarest and most sought-after appearances.

Gems are obtained through real-world money purchases, trading in-game gold, and obtaining significant numbers of achievement points. Since in-game gold can be traded for gems, this means that anything you can get from buying gems with real-world money can also be bought by converting in-game gold to gems.

Items offered in the Gem Store fit into one of the following categories:

• Cosmetic items only affect appearances. These include things like such as weapon or armor skins, outfits, finishers, mail carriers, makeover kits, dye packs, or miniatures.
• Convenience items allow players to do things in a faster or more convenient way. These include infinite-use gathering tools, instant bank access, a home instance teleporter, reward boosters, and revive orbs (usable only in PvE).
• Upgrade items expand your account. These include additional character slots, bank space, inventory bag slots, or crafting licenses. The digital deluxe upgrade and living-story unlocks (for ones that you missed getting for free) are also included.
• Amusement items can have interesting effects on the player and others. These include items such as ones that bestow random transformations, make everyone appear to be a bobble-head, allow you to start a water balloon fight, or provide additional dance moves, and also musical instruments.
• Other items also exist, such as keys to get random items, items that increase durations of nourishments, and toys.

There are a few "competitive" advantages to be gained, but these are minor, and none affect sPvP:

• Some boosters that are obtainable from Black Lion Chests can give increased running speed, attack strength, regeneration, or armor for one hour. These can only be used in PvE and WvW, and are non-problematic in WvW due to its large-scale, casual nature.
• Some toys can be used for costume brawl, and are often more powerful than costume brawl transformations obtained through other means. Costume brawl is generally silly and unbalanced, even without considering gem store items, so this isn't really a "competitive" advantage.
• The digital deluxe upgrade is the only way to unlock the Mistfire Wolf elite skill, which is only useable in PvE and WvW.
• Living World Season 2 is required to get ascended trinkets with Nomad's or Sinister stats.

It's also important to note that all players' stats are equalized for sPvP, regardless of level or gear.

TL;DR : Guild Wars 2 isn't pay to win but pay to look pretty.

You can indeed use real money to get in game gold, however the gear you can aquire with this gold has the same stats than lower priced gear with the same rarity. This come from the fact that stats on gear don't have random values but fixed values. Which means you can buy an exotic weapon for 1 gold that would have the exact same stats as another exotic that cost 300 gold. The difference in price come from the skin an equipement has. Some skins are more rare/desirable thus more expensive.

Exception made of legendary weapons which have slightly better stats than exotic weapons. However,not everyone has a legendary weapon and you shouldn't be concerned about those for a long time.

There is an in game store that provide a lot of cosmetic items and quality of life improvement (more space in inventory, more character's slots, easy travel accross the map, etc.) but nothing gamebreaking and allowing to get an advantage over other players. The money you put into Guild Wars 2 will be before anything for Character's customisation.

No it is not. No items offered by the Gem Store offer any in-game advantage at all.

Items sold in the Gem Store for real money are all convenience or cosmetic in nature. It was a founding principle of the game that you should not be able to gain an advantage by paying money.

You can find out more about the Gem Store on the wiki.