This paper proposes a NOMA-assisted uplink xURLLC network architecture that integrates a stochastic network calculus (SNC)-based statistical quality of service (SQP) framework (SNC-SQP) to analyze the tail distributions of key performance indicators (KPIs) such as delay, age-of-information (AoI), and reliability. The SNC-SQP framework provides theoretical insights into SQP performance by defining statistical delay violation probability (SDVP) and statistical AoI violation probability (SAVP), and deriving their upper bounds. Based on SNC-SQP, an SQP-driven power optimization problem is formulated to minimize uplink transmit power while guaranteeing xURLLC's KPIs. Extensive simulations validate the proposed framework, showing that the power allocation scheme significantly reduces uplink transmit power and outperforms conventional schemes in SQP performance. The paper discusses the challenges of achieving ultra-reliable, low-latency, and high-freshness (AoI) communications in xURLLC, including co-channel interference, tail probability analysis, and power allocation. It introduces the SNC-SQP theoretical framework to address these challenges, providing a principled approach for analyzing the tail distributions of KPIs and ensuring SQP performance. The framework is applied to a NOMA-xURLLC network architecture, which includes a physical layer, queuing layer, and control layer. The physical layer handles short-packet communications, the queuing layer manages packet buffers and SQP requirements, and the control layer ensures power allocation and SQP performance. The paper evaluates the performance of the proposed NOMA-xURLLC network architecture through simulations, demonstrating its effectiveness in reducing uplink transmit power and improving SQP performance. The results show that the proposed power allocation scheme outperforms conventional orthogonal multiple access (OMA) schemes in terms of SQP performance, particularly for short packets with stringent delay and AoI requirements. The study also highlights the importance of tail probability analysis in xURLLC and the potential of SNC theory in providing reliable theoretical insights for SQP performance. The paper concludes with future research directions, including flexible interference management for massive xURLLC, security of xURLLC, and predictive xURLLC with machine learning.This paper proposes a NOMA-assisted uplink xURLLC network architecture that integrates a stochastic network calculus (SNC)-based statistical quality of service (SQP) framework (SNC-SQP) to analyze the tail distributions of key performance indicators (KPIs) such as delay, age-of-information (AoI), and reliability. The SNC-SQP framework provides theoretical insights into SQP performance by defining statistical delay violation probability (SDVP) and statistical AoI violation probability (SAVP), and deriving their upper bounds. Based on SNC-SQP, an SQP-driven power optimization problem is formulated to minimize uplink transmit power while guaranteeing xURLLC's KPIs. Extensive simulations validate the proposed framework, showing that the power allocation scheme significantly reduces uplink transmit power and outperforms conventional schemes in SQP performance. The paper discusses the challenges of achieving ultra-reliable, low-latency, and high-freshness (AoI) communications in xURLLC, including co-channel interference, tail probability analysis, and power allocation. It introduces the SNC-SQP theoretical framework to address these challenges, providing a principled approach for analyzing the tail distributions of KPIs and ensuring SQP performance. The framework is applied to a NOMA-xURLLC network architecture, which includes a physical layer, queuing layer, and control layer. The physical layer handles short-packet communications, the queuing layer manages packet buffers and SQP requirements, and the control layer ensures power allocation and SQP performance. The paper evaluates the performance of the proposed NOMA-xURLLC network architecture through simulations, demonstrating its effectiveness in reducing uplink transmit power and improving SQP performance. The results show that the proposed power allocation scheme outperforms conventional orthogonal multiple access (OMA) schemes in terms of SQP performance, particularly for short packets with stringent delay and AoI requirements. The study also highlights the importance of tail probability analysis in xURLLC and the potential of SNC theory in providing reliable theoretical insights for SQP performance. The paper concludes with future research directions, including flexible interference management for massive xURLLC, security of xURLLC, and predictive xURLLC with machine learning.