Is he the current “leader” and can he take any official actions against those he sees as to blame for this apparent failing?
US political parties don't necessarily work like that. You affiliate with a party by choice, and the party, in turn, offers you national resources (Congressional race funds, gubernatorial race funds, etc). While a party can actively remove you from power within the party, there's no de-facto leader. Instead, "leadership" often falls to the highest elected officials within the party. Lose an election, and you lose your standing within the party. In 2014, Republican Eric Cantor (then House Majority Leader) lost his primary. He subsequently stepped down as Majority Leader. This note in the article is of great importance
Cantor did not say what he will do next, but told the Richmond newspaper paper that he will continue to be active in some way in private life and advocate for the causes he believes in.
In other words, you can stay in power as long as you win (there are some exceptions to that, like Speaker John Boeher resigning after internal party dissention, but they are rare).
What power does Trump wield?
Trump lost the 2020 election, but he's in an unusual position within the Republican Party
- There's no other clear Republican leaders. Mitch McConnell (Senate Minority Leader) would probably be the closest thing to one right now. Kevin McCarthy (House Minority Leader and potentially Speaker in 2023) has never regained the same standing he once held since his 2015 gaffe in his bid to replace Boehner.
- Trump is a likely Presidential candidate in 2024 (he continues to hint he will announce his bid soon). Since he was an elected President, he still has some prominence in the media.
- Trump still polls well among the GOP. Mind you, the 2024 race has not started so this is a "Trump vs anyone else" poll, but Five Thirty Eight shows Trump topping all 2024 contender polls. That still gives him something of a bully pulpit (an effect enhanced by social media)
- Trump endorsements. This really needs more than just a footnote, however...
Trump endorses people
In the 2022 cycle, Trump went around endorsing people, particularly if they sought his endorsement. Axios has a good rundown (mind you, a number of races are currently uncalled), but Trump made calls that were good for Trump, at least. Let's look at some microcosms from 2022
JD Vance - Ohio Senate - You'll note that article starts with "Trump-backed JD Vance", which really typifies a lot of endorsements. But Vance was running in a deep-red state. It's unclear how much Trump impacted this race. Still, Vance actively sought Trump's backing in the primary and openly endorsed Trump's "stolen 2020 election" narrative.
Kari Lake - Arizona Governor - As of this writing, Lake is slightly behind with 76% reporting. This state went slightly for Biden in 2020. Lake has also openly endorsed the 2020 narrative, and has been more full-throated about it than Vance. If Lake wins, it will be a very narrow victory for her.
Mehmet Oz - Pennsylvania Senate - Unlike other races (where Trump's endorsement is harder to quantify), Trump's endorsement likely put Oz over the top in a very close primary
Landing former President Donald Trump’s endorsement was vital for Oz, though he still had to conquer doubts about his conservative bona fides among the party base. Trump levied attacks against Oz’s rivals, portrayed him as the best candidate to win in November, and pushed Oz to declare victory before a winner was determined.
As Oz's opponent, John Fetterman, noted, Oz was a carpetbagger: Oz had not lived in the state for very long, nor had he been a longtime member of the GOP. Oz lost the general election by 5 points.
Mo Brooks - Alabama Senate - This is noteworthy because Trump endorsed Brooks early on, largely because Brooks had endorsed him early in his 2016 cycle. As with fellow Alabamian Jeff Sessions (former Senator who was fired by Trump from his US Attorney General appointment), Trump soured on Brooks when Brooks began to falter in the polls
In a statement, Trump cited Brooks’ languishing performance in the
race and his attempt to move Republicans beyond Trump’s false 2020
election fraud claims. The former president said he will make another
endorsement in the “near future.”
“Very sad but, since he decided to go in another direction, so have I,
and I am hereby withdrawing my Endorsement of Mo Brooks for the
Senate,” Trump said.
Brooks responded that he had not changed at all, and he accused Trump
of dropping him for rebuffing the former president’s entreaties —
coming as recently as last week — to help overturn the 2020 election.
“He wanted the election rescinded and a do-over,” Brooks told
reporters in Alabama. “But there’s no legal way to do it.”
Trump subsequently endorsed Katie Britt, who was the front runner and easily won both the primary and general election in a deep red state.
Trump wields some power within the GOP still, owing to his fervent base. After the 2022 midterms (where Trump played some role), that power may be diminished. It remains to be seen if the GOP rejects Trump in future elections. Trump has no official role because no official role exists.