The statement accurately reflects India's deep-seated concerns regarding the situation in Afghanistan, particularly in the context of the US withdrawal and the subsequent rise of the Taliban. The war in Afghanistan has indeed been crucial for India's national security, and the implications of a Jihadi resurgence are profoundly worrying.

Cruciality for India's National Security:

1. Geopolitical Proximity: Afghanistan shares a historical and geographical proximity with India, making developments there directly impactful on India's security calculus. Instability in Afghanistan often spills over into the wider South Asian region.
2. Terrorism and Radicalization: India has historically been a victim of terrorism emanating from groups operating from or supported by elements within Afghanistan and Pakistan. A Taliban-controlled Afghanistan, especially one that provides safe havens to various Jihadi groups, directly threatens India. Groups like Lashkar-e-Taiba (LeT) and Jaish-e-Mohammed (JeM), which have targeted India, could find renewed sanctuary and operational freedom.
3. Regional Instability: A chaotic or Taliban-dominated Afghanistan can destabilize the entire region, impacting Central Asian republics, Iran, and Pakistan, which in turn affects India's strategic interests and connectivity projects (e.g., Chabahar Port).
4. Drug Trafficking: Afghanistan is a major producer of opium. Instability often leads to an increase in drug production and trafficking, which can fuel terrorism and organized crime, posing a threat to India's internal security and public health.

Impact of US Withdrawal and Jihadi Triumphalism:

1. Resurgence of Terror Groups: The US withdrawal created a power vacuum that the Taliban swiftly filled. This triumphalism emboldens not only the Taliban but also other associated Jihadi groups, including Al-Qaeda and ISIS-K, who see it as a victory against a global superpower. These groups could use Afghanistan as a base to plan and execute attacks against India, potentially reviving the 'arc of terror' that India has long feared.
2. Cross-Border Terrorism in Kashmir: India has consistently highlighted Pakistan's role in sponsoring cross-border terrorism in Jammu and Kashmir. A Taliban-controlled Afghanistan could provide a strategic depth and training ground for Pakistan-backed terror groups, leading to an escalation of violence in Kashmir. The return of battle-hardened fighters from Afghanistan could further exacerbate the situation.
3. Radicalization and Extremism: The success of the Taliban could inspire and radicalize extremist elements within India and the broader region. The narrative of 'Jihadi victory' can be a potent tool for recruitment and propaganda, posing a significant challenge to India's secular fabric and internal security.
4. Loss of Indian Influence and Investments: India has invested significantly in Afghanistan's development, building infrastructure, and providing humanitarian aid. A hostile regime could jeopardize these investments and diminish India's influence in a strategically important country.
5. Proxy Warfare: A Taliban-led Afghanistan, potentially influenced by Pakistan, could become a platform for proxy warfare against India, using various terror outfits to destabilize the region without direct state involvement.

In conclusion, the statement is highly pertinent. The developments in Afghanistan post-US withdrawal have indeed created a precarious security environment for India. The resurgence of Jihadi groups, emboldened by their perceived victory, poses a direct and significant threat of increased terrorism, radicalization, and regional instability, demanding a vigilant and multi-pronged security and diplomatic response from India.