According to Western sources, Putin has managed to keep a lid on Chechnya by allowing Kadyrov a large degree of political autonomy in internal matters, which resulted in a significant 'Islamization' of Chechnya's government policies, e.g.:
Most women on the streets of Grozny, the capital, wear the Islamic hijab, a dress code until recently enforced by drive-by paintball shootings. [...] And, lest they forget, a building-size poster on Grozny’s main thoroughfare, Vladimir Putin Avenue, carries an example of proper attire. It is inscribed with Mr. Kadyrov’s admonition that the “hijab protects the dignity of the Chechen woman.”
Alcohol, officially allowed for sale only between 8 a.m. and 10 a.m. since 2009, has become virtually unavailable. Ostentatious new mosques are mushrooming, lessons in Islam are mandatory in schools, and the government sponsors youths who memorize the Quran.
Mr. Kadyrov fills his Instagram feed—his main means of communication—with footage of himself performing prayers and urging piety. His biography is a pithy one-liner: “Love the Prophet, read the prayers.”
Aslan Abdullayev, the deputy mufti, or religious leader, of Chechnya, noted with pleasure that the level of Islamic observance here is much higher than it was in the 1990s, when the republic was de facto independent and a magnet for jihadists from around the world.
So, that theory goes, Russia thus managed to somewhat placate the more extremist elements in Chechnya (in a manner that's not too far from how Saudi Arabia or Pakistan turned more Islamic/conservative [for decades], in the late 1970s.)
Ostensibly though, that is done in Chechnya thorough personal/cultural examples, and not through any [Sharia-like] laws:
“We are a normal secular republic. Russian laws are sacred to us,” said Djambulat Umarov, the minister of national policy, external relations and information. “But if you follow Kadyrov’s path, the path of creation, the path of returning to cultural values, then you are a Muslim and you must be an example in everything—and you should follow to the maximum the sacral truths, including in matters like clothing and chastity.”
How is the situation in Tajikistan though? Are they more liberal than Chechnya in re Islamic symbology, so that gives more room for extremists to use as a grievance to recruit there?
(FWTW, aside, the gov't in Dushanbe claims that most Tajiks that were IS-radicalized, were so while visiting Russia, at least between 2014-2016.)