Spin-boson models are simple examples of quantum dissipative systems, but also serve as effective models in quantum magnetism and exhibit nontrivial quantum criticality. Recently, they have been established as a platform to study the nontrivial renormalization-group (RG) scenario of fixed-point annihilation, in which two intermediate-coupling RG fixed points collide and generate an extremely slow RG flow near the collision. For the Bose Kondo model, a single S =(Formula presented.) spin where each spin component couples to an independent bosonic bath with power-law spectrum (Formula presented.) ω^s via dissipation strengths α_i, i (Formula presented.) {x, y, z}, such phenomena occur sequentially for the U(1)-symmetric model at αz = 0 and the SU(2)-symmetric case at αz = α_xy, as the bath exponent s < 1 is tuned. Here we use an exact wormhole quantum Monte Carlo method for retarded interactions to explore how this nontrivial fixed-point structure affects the phase diagram and phase transitions of the anisotropic spinboson model. In particular, we show how fixed-point annihilation within a symmetry-enhanced critical manifold leads to a variety of anisotropy-driven critical phenomena: (i) a continuous order-to-order transition beyond the Landau paradigm, (ii) a symmetry-enhanced first-order transition, and (iii) pseudocriticality. Depending on whether the attractive fixed point within the critical manifold corresponds to a critical or a localized phase, the transition between the two long-range ordered localized phases can be tuned from continuous to strongly first order and even becomes weakly first order in an extended regime close to the fixed-point collision. We extract critical exponents at the continuous transition, but also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent s. Moreover, we provide direct numerical evidence for pseudocritical scaling on both sides of the fixed-point collision, which manifests in an extremely slow drift of the correlation-length exponent, even at the continuous transition. In addition, we also study the crossover behavior away from the SU(2)-symmetric case and determine the phase boundary of an extended U(1)-symmetric critical phase for α_z < α_xy. Our work establishes the spin-boson model as a paradigmatic example to access tunable criticality and pseudocriticality across the fixed-point collision in large-scale simulations, which is reminiscent of a scenario discussed in the context of deconfined criticality.